The anti-Tinder! 33-year-old virgin who chose to become abstinent at age 13 launches dating app for people who DON’T want to have sex
Shakia Seabrook, 33, from Tampa, Florida, started ‘The Sexless Tribe’ last year as a hub for the sexually abstinent – a community she said that’s underrepresented
The woman, who made the decision to be abstinent at 13, said making the app was her ‘calling,’ and that she started it after she realized it was what God wanted
She explained that The Sexless Tribe is more than just a dating app, it’s also a place where abstinent people can ‘come together and connect’
Per its website, The Sexless Tribe App ‘makes it easy for sexually abstinent people to access abstinence resources, make romantic connections, and more’
She uses the platform to remind its 8,000 subscribers that if ‘they’re having a little itch, they can go to the app and listen to a song or a video or a podcast’
She also uses the app to send ‘encouraging messages,’ provide resources, and host virtual events
A woman has created a dating app solely for people who aren’t having sex, after she said God ‘called to her’ and asked her to make it.
Shakia Seabrook, 33, from Tampa, Florida, started ‘The Sexless Tribe’ last year as a hub for people who are sexually abstinent – a community she thought was being underrepresented.
The entrepreneur, who made the decision to be abstinent when she was 13 years old, explained that it’s more than just a dating app – but that it’s also a place where abstinent people can ‘come together and connect.’
Per its website, The Sexless Tribe App ‘makes it easy for sexually abstinent people to access abstinence resources, find accountability partners, form friendships, and make romantic connections.’
Shakia, who said it was her ‘calling’ to make the app, uses the platform to give its 8,000 subscribers ‘encouraging messages’ and ‘late-night check-ins,’ and to remind them that if ‘they’re having a little itch, they can go to the app and listen to a song or a video or a podcast.’
‘This lifestyle isn’t talked about enough. It’s not visible enough,’ said Shakia.
‘There’s not space enough for people to come together and get the help they desire to be successful in living this lifestyle, so I arose to the challenge.’
A woman has created a dating app solely for people who aren’t having sex after she said God ‘called to her’ and asked her to make it
Shakia Seabrook, 33, from Tampa, Florida, started ‘The Sexless Tribe’ as a hub for people who are sexually abstinent – a community she thought was being underrepresented
Per its website, The Sexless Tribe App ‘makes it easy for sexually abstinent people to access abstinence resources, find accountability partners, and make romantic connections’
The entrepreneur explained that it’s more than just a dating app – but that it’s also a place where abstinent people can ‘come together and connect’
Shakia explained that although she wasn’t ‘super passionate’ about abstinence at first, she decided to go ‘full throttle’ with the app after she said she realized it was what God wanted of her.
‘God just kept showing me this is what I’m calling you to do,’ she said.
‘I pushed back against it because it wasn’t a topic that I was super passionate about. In 2020, I finally gave God my yes and went full throttle from then on out.
‘I started [with] T-shirts and then I realized it wasn’t enough because people wanted community.
‘I came across someone that had created an app and I was like that’s what we need: we need a home, we need a place that we can come together and connect.’
The app consists of two parts: a resource space for abstinence-based material and TST social – a community space where users can create profiles and interact.
‘In September 2020, I created the community space,’ Shakia said.
‘Then, I realized that wasn’t enough because people were still DMing me asking [if] I knew any books, or podcast, or YouTube channels about abstinence.
‘I realized that they also needed resources and in the beginning of this year I created the resources part of the app and now it’s one big hub.
‘There are events that are hosted in the app every month via Zoom. Every day they get an encouraging quote to their phone, and they get a late-night check-in just to hold them accountable.
‘I tell them at night – maybe you’re having a little itch, maybe you need to go to the app and listen to a song or a video or a podcast.’
Though the app is still in beta mode, Shakia said there have been over 8,000 downloads for both parts already, and people use them globally.
‘We literally have people from all over the world that will stay up for the events. Some people will get up at four in the morning just to get on,’ she said.
‘Africa, the UK, India, Australia – I’ve shipped out to Ireland and Israel. All over, people are tapping in whether it’s on the app, via the store, or even a YouTube channel.’
Though she is a Christian, Shakia said her decision to remain abstinent wasn’t rooted in religion.
‘Even though I’m a Christian, my “why” wasn’t initially rooted in God, but it’s matured more over the years and God now is a part of that foundation,’ she said.
‘I can remember as early as 13 making the decision. I don’t know why I made that decision at 13, but as I got older, seeing how casual sex was happening, it was nothing I desired.
‘It didn’t look super special and fun. The right person is a man that stands before me, God.’
Shakia also said that the app isn’t exclusively for Christians, and that she wants people to know that everyone is welcome.
‘Some people ask, “Is it a Christian app?” It’s not a Christian app. “I’m not a virgin can I join?” Absolutely,’ she said.
‘All are welcome. I didn’t create it only for Christians, I created it for anyone who’s living this lifestyle.’
Shakira also likes to post videos about her lifestyle online, and although she’s gotten no negative feedback about the app, she said people do react negatively to the clips.
‘I do get backlash from videos I make, especially about me being a virgin,’ she said.
‘Which blows my mind because if you watch any of my videos. I tell people I’m not here to convince, condemn or convict. I’m just sharing my truth.
‘I’m literally just saying a fact that’s true to me, but somehow people are saying I’m imposing my beliefs on other people or I’m shaming people who are non-virgins.’
She also said that the app isn’t exclusively for Christians, and that she wants people to know that everyone is welcome. ‘I created it for anyone who’s living this lifestyle,’ she added
Shakia explained that her goal is to ‘stand as the voice and let people know that there is an option.’ She said: ‘the time that we’re living in there’s only one option being pushed and it’s sex’
Shakia insisted she isn’t there to judge but to ‘stand as the voice and face and let people know that there is an option.’
‘I feel like in order to make an informed decision with anything you have to be informed of all the options and I think the time that we’re living in there’s only one option being pushed and it’s sex,’ she said.
‘If people choose to do that, I don’t have anything to say about it, I just think we’re doing a disservice to the youth.
‘When I was 13, I needed to know that living an abstinent lifestyle is doable and it’s being done.
‘A lot of youth will reach out to me and ask me, “Can I wait?” and that blows my mind that they think that’s something they have to ask.
‘I just love being able to allow people to see that there is a different option and really give a new face and voice to what it’s like to live abstinent.
‘People think they know what a virgin looks or acts like, so just showing them that we’re out here and we’re cute and we’re living and we’re fun, but we just made a decision in regard to our sexuality.”


Founded in 1896, F. Hoffmann-La Roche AG is a Swiss-based global pharmaceutical firm with a purpose to do now what patients need next. In late 2020, as part of accelerating innovation for more than 100,000 Roche employees and a global network of business partners, the company signed a five-year agreement with Google Workspace to extend their partnership.
24 Nov 2021 Posted in Platform Infrastructure
The Roche journey using Google Workspace began with Gmail and Calendar
In 2012, Roche chose Google Workspace as its foundational platform to drive collaboration and innovation. Google Workspace’s unique ability to provide secure, real-time, multi-device collaboration was critical to Roche as they began to integrate Google Calendar and Gmail into their global enterprise IT solutions.
Roche continues to fuel innovation with Google Workspace in 2021 and beyond
Based on the impact Roche saw with Google Workspace, the company expanded its adoption of the collaboration solution to include Google Meet, Slides, Sheets, and Google Cloud Search.
Google Workspace has also been foundational as Roche extends its agile transformation journey across all regions and value chains. This includes establishing cross-functional teams across the organization and around the world, helping to break down silos and drive co-creation and accelerate innovation.
Moving from corporate office to virtual office
Because of its investments in Google Workspace, Roche was in a strong position to shift seamlessly to remote work when the pandemic occurred. A secure, work-from-anywhere environment meant that tens of thousands of employees, contractors, and suppliers whose physical presence wasn’t required on site could make the pivot, with the access to the information—and each other—they needed to be successful. And they could also stay connected to those who needed to be on site, in the laboratories and manufacturing divisions. Within days of the transition, Roche saw an increase of more than 600% in virtual meetings over Google Meet as new ways of working became commonplace.
The road ahead
As the technology landscape and the world of work continue to evolve, the relationship between Roche and Google Workspace is strengthened by a common desire to innovate in the face of change. For Google Workspace, Roche represents a growing number of clients, from startups to global enterprises, who are looking to transform how employees connect, create, and collaborate—wherever and however they work.
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Angular is currently one of the most used front-end frameworks. Even though it provides a lot of out-of-the-box features that enforce good practices, you still need to know these four design tips to keep your application clean, sustainable, and scalable.
The guidelines presented below will help you design high-performance applications where continued development is sustainable and scalable as the complexity of the application increases.
1. Organize Your Code
Organizing features and modules is crucial when building an Angular application. Team members should be able to locate the code quickly, so keep your folder structure as flat as possible. It is also important that the code snippets can be identified swiftly. This can be easily accomplished by adding the component's functionality to its name following this recommended pattern: feature.type.ts, as shown below:
Image courtesy of Angular
Using this feature-based approach to structure your code will make it DRY, reusable, and easy to maintain. Try to have at least one module per feature. Usually, a well built application is divided into a core module, a shared module, a routine module, and feature modules. Let's review each module type.
CORE MODULE
The core module is designed for singleton services that any element in the application can use. We don't want to import this type of service in each module, since this will create additional instances. Some examples of singleton services are LoggingService, ErrorService, and DataService. The core module must be imported only once by the root module to ensure that we can add a conditional inside the constructor to check it.
export class CoreModule {
  constructor(@Optional() @SkipSelf() parentModule: CoreModule) {
    if (parentModule) {
      throw new Error(
        'CoreModule is already loaded. Import it in the AppModule only'
      );
    }
  }
}
SHARED MODULE
The shared module is designed for common components, services, and other modules that will be used across multiple features. Usually this module is where we declare our Pipes, Directives, and other template components that are commonly used across the application, like a CalendarComponent and CurrencyPipe.
ROUTING MODULE
The routing module defines routes and provides the routing configuration. It creates the experience of a multiple-page application in a single-page application by allowing the user to navigate between different components after some events. It adds router configuration to the module's import and separates routing concerns from its companion module.
FEATURE MODULE
In addition to the modules detailed above, we can create other functionalities as feature modules. A feature module helps you to partition the app into focused areas, and it collaborates with the root module and with other modules through the services it provides and the components, directives, and pipes that it shares. This also enforces the single responsibility principle since a feature module must be designed to have one well-defined purpose. In fact, a hallmark of poorly-written code is modules that have more than one responsibility. So when you notice that one of your modules is getting bigger or too complex, consider splitting it into two or more modules with well defined roles.
TYPICAL ORGANIZATION
The image below shows a typical way to define your modules. In general, widgets and pipes go into the Shared Module, services go into the Core Module, and routed components go into the Routing Module. The exception is when one of these is specific to a feature.
Architecture aside, there are a few specific changes that can improve your application's performance.
2. OnPush Change Detection Strategy
Angular Change Detection Strategy encompasses the methods by which the updates to the component are tracked and the component is triggered to Re-render. The purpose of this mechanism is to put the views in sync with their model. This model change can be triggered by a DOM event, an AJAX request, or timers.
On the Default Change Detection Strategy, every time a DOM event, an AJAX request, or a trigger by setTimeout or setInterval happens, Angular will verify if there was any change between the previous and the current state of the overall application model. This strategy is less efficient since the DOM is often re-rendered on child components, even if the change detected only affects the parent component.
This doesn't happen on the OnPush Detection Strategy. When using OnPush, whenever a parent element is updating values that are not passed as an input property to the child component, the child component will not be checked and re-rendered. So it's recommended to use the OnPush strategy on child components when they only depend on its inputs.
import {ChangeDetectionStrategy, Component} from '@angular/core';
@Component({
  // ...
  changeDetection: ChangeDetectionStrategy.OnPush
})
But the OnPush strategy can be tricky! When using OnPush Change Detection Strategy, we must work with immutable objects. If we don't, we might cause some bugs that are really hard to track. So in order to trigger a change detection in our component, whenever our input is an object or array, we need to change their reference. For example:
mutable -> this won't trigger the detection strategy
arr.forEach((num, index) => {
   return arr[index] = num * 2;
});
immutable -> this will trigger the detection strategy because the reference for the array was changed
arr = arr.map(num => {
   return num * 2;
});
3. Pipes Instead of Method Calls on the Template
@Component({
  template: `
...

Welcome !

...
  `
})
export class UserComponent {
  @Input() user: { firstName: string, lastName: string };
  constructor() { }
...
  fullName() {
    return this.user.firstName + ' ' + this.user.lastName
  }
...
}
When we add a method call on the template, it can be executed several times, which will reduce the performance of the application. This happens because the method will be called every time the change detection runs. So if change detection runs 100 times, the function is called 100 times, even if the change happened in a part of the code that is not related to this method call.
There are two simple ways of solving this issue. One of them is calling the method on your component's controller and assigning the result to a variable that will be used on the template.
@Component({
  template: `
...

Welcome !

...
  `
})
export class UserComponent {
  @Input() user: { firstName: string, lastName: string };
  fullName = '';
  constructor() {}
 ngOnChanges(changes: SimpleChanges) {
    if (changes.user) {
      this.fullName = this.calculateFullName();
    }
  }
...
  fullName() {
    return this.user.firstName + ' ' + this.user.lastName
  }
...
}
Another way to accomplish this is by using Pipes. A pipe is a way to transform a value for display on the template without transforming it in your controller. It takes your data as an input and transforms it to a desired output. A pure pipe is a function with the return value depending only on arguments that are passed to the function. Unlike a method call, a pure pipe transform is called only when the parameters change. This way, instead of being called several times, a pipe will be called only once.
@Pipe({
  name: 'fullName',
  pure: true
})
export class FullNamePipe implements PipeTransform {
  transform(user: any, args?: any):any {
    return user.firstName + user.lastName;
  }
}
@Component({
  template: `
...

Welcome !

...
  `
})
export class UserComponent {
  @Input() user: { firstName: string, lastName: string };
  constructor() {}
}
4. Lazy Loading Feature Modules
By default, when the application starts, all of its modules are loaded at once, even though they are not immediately needed. One advantage of splitting the application into modules is the ability to load certain modules only when they are required, which keeps the initial bundle size smaller and helps the application to load faster.
To lazy load Angular modules, use loadChildren (instead of component) in your AppRoutingModule routes configuration.
const routes: Routes = [
  {
    path: 'lazy',
    loadChildren: () => import('./lazy/lazy.module').then(m => m.LazyModule)
  }
];
Don't forget to remove the ItemsModule from the AppModule, otherwise it will be loaded when the application bootstraps.
Summary
There are still several topics we haven't covered in this article, but these four tips are a good place to start, particularly for developers who are newer to designing Angular applications. These tips may also be used to improve existing applications since there's always room to make our code stronger!
Questions or comments? Share your experience below!
References
Angular coding style guide
Angular: Organizing Features and Modules
Angular - Core and Shared Modules
Angular Best Practices
Angular Change Detection and the OnPush Strategy
Angular Change Detection - How Does It Really Work?
Author
Suelen Romano
Suelen Romano is a Front-end Developer at Avenue Code. She enjoys playing with her pets, watching reality shows, and traveling.


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In order to check if a process Impl refines (in a particular semantic model) a process Spec, FDR firstly converts Impl and Spec into labelled transition systems, as described in Compilation. FDR then normalises the specification machine, as described in normal. FDR then explores the states of these processes in breadth-first order, checking that the states are related according to the semantic model. As soon as FDR finds a counterexample it immediately reports it. Thus, thanks to the breadth-first order, any counterexample that FDR returns will be minimal in the length of the trace (including taus).
In order to understand exactly how FDR visits state pairs during a refinement check, consider the following script:
channel a, b, c

P1 = a -> P2
P2 = P3 |~| P4
P3 = b -> P2
P4 = a -> P1

Q1 = a -> Q2
Q2 = b -> Q1

assert Q1 [T= P1
FDR initialises the search by looking at the state pair (Q1, P1) (nb. state pairs consist of a specification state and an implementation state). In the traces model, FDR only has to check that the events (excluding tau) offered by P1 are a subset of those offered by Q1, which is clearly the cases here. Hence, FDR now adds the successor state pairs for each event offered by P1 to the search. In this case, there is only one successor state pair after a, (Q2, P2).
When considering the state pair (Q2, P2) note that P2 does not offer any visible events, and therefore the event check is trivially true. FDR now needs to add any new state pairs to the search. In this case, the two state pairs (Q2, P3) and (Q2, P4) are added to the search. Note that the specification part of the state pair is kept the same because the implementation performs a tau. FDR will now consider the new state pairs. In particular, when it considers (Q2, P4) FDR will find a counterexample since the events offered by P4 are not a subset of those offered by Q2.
In order to reconstruct the trace that the invalid state pair was reached by, FDR stores a parent state pair of each state pair that it finds during the search. Thus, in the above example, FDR will set the parent of (Q2, P4) as (Q2, P2) and the parent of (Q2, P2) to (Q1, P1). Thus, FDR can reconstruct the counterexample trace by finding events that transition between (Q1, P1) and (Q2, P2), and (Q2, P2) and (Q2, P4). This will yield the trace <a, tau>, in this case.
Counterexamples¶
A counterexample to a refinement assertion consists of a trace leading to a particular state pair that are not related according the to semantic model in use. Thus, if the traces model is in use, then this must mean that the implementation can perform an event that the specification cannot. If the failures model is in use, then either the above case applies, or the implementation can refuse a set of events that the specification cannot. If the failures-divergences model is in use, then this must mean that either one of the above cases applies, or the implementation is divergent but the specification is not.
Uniqueness¶
If FDR is asked to generate multiple counterexamples then this motivates the question of what FDR considers distinct counterexamples to be. In all cases, only a single counterexample will be generated from a single state pair. Thus, if a state pair is reachable via two different traces then only one counterexample will be generated, regardless of the number requested. Further, once FDR has found a counterexample for a given state pair, it does not look at successors of the state pair to see if they are counterexamples. Thus, for FDR to report two distinct counterexamples the counterexamples must be distinct state pairs, and the second state pair must be reachable via a path that does not include the first state pair. For example, the following has two counterexamples since the two STOP states are reachable via distinct paths:
P1 = STOP |~| P2
P2 = STOP

assert P1 :[deadlock free [F]]
However, the following only has one counterexample, since the second invalid state pair is only reachable via the first invalid state pair:
P1 = a -> P2 [] b -> STOP
P2 = a -> P1

Spec = a -> Spec

assert Spec [T= P1
Note that both P1 and` P2 violate the property, but P2 is only reachable via P1 and thus is not considered.
Non-Determinism¶
As noted above, thanks to the breadth-first ordering that FDR visits the state pairs in, FDR will always pick the counterexample that is reachable in the fewest events (either tau or a visible event). Whilst this might imply that the counterexample returned is chosen deterministically, this is not the case when FDR is being used in parallel mode (i.e. refinement.bfs.workers is greater than 1) for two reasons:
The predecessor state pair of each state pair is chosen by a race between the different processor cores on each ply. For example, if two different cores both discover the same state pair on the same ply, then the state pair that is marked as the new state pair’s predecessor is chosen non-deterministically. This can result in a different trace being returned. The following script should exhibit this behaviour:
channel a, b, c

P = a -> b -> Q [] b -> a -> Q
Q = c -> STOP

R = a -> R [] b -> R [] c -> R

assert R [F= P
Note that there is precisely one state that violates the refinement, Q, but there are two different routes to Q, via either <a, b> or <b, a>. Hence, since the states b -> Q and a -> Q are discovered on the same ply of the breadth-first search the winner will be chosen non-deterministically (assuming that they are visited by different cores). This should result in FDR non-deterministically returning either the counterexample trace <a, b, c> or <b, a, c>.
On each ply of the search, there is essentially a race between the processor cores to find a counterexample: the first core that finds a counterexample wins. For example, consider the following refinement check:
channel a, b

P = a -> STOP |~| b -> STOP

assert STOP [T= P
There are two different counterexamples to this assertion: either the event a can be performed, or the event b. Since these counterexamples are both found on the second ply of the search (the first ply simply explores the tau transitions available from the starting state), FDR will pick the counterexample non-deterministically, providing the two different states are picked by different cores.
In general use, the fact that different counterexamples are produced should hopefully not be an issue. Unfortunately, there is no efficient way to make a parallel version of FDR deterministically return the same counterexample. If it is important that the same counterexample is returned each time then refinement.bfs.workers should be set to 1, thus disabling the parallel refinement checker. This will obviously result in a decrease in performance, but it does mean that the same counterexample will always be returned.


The Intel Iris Xe is one of the most popular graphics processors available in late 2020 laptops due to its integration into Gen Intel Core i5 and i7 G7-series main processors. This configuration is ideal for playing the new slot games coming soon, allowing you to enjoy the best graphics and gaming experience available today!
Iris Xe is the name given to the new integrated graphics built into the upper tier of Intel’s 11th generation laptop chips. The Iris Xe will be included in two of Intel’s latest processors — Core i5 and i7.
Here is a summary of the new chips from Intel:
Intel claims that these chips will roughly double the graphics performance of the previous generation. If these claims prove true, Intel has made a massive step in gaming capabilities for thin-and-light laptops. With Intel’s 11 Generation of mobile processors, you’ll experience new levels of performance to real-world workflows and experiences. Iris Xe delivers transformational graphics and vivid media for creating, gaming, and entertainment on a thin, light laptop PC.
The Future of Graphics
Although Iris Xe took a big step in the GPU space, the company looks to make an even bigger splash in 2021 by releasing its first discrete graphics card for PC gaming.
But for now, the possibility of having laptops capable of handling 1080p gaming in the mass-market could be a considerable development for Intel and those looking to have power without sacrificing portability.
Perhaps, for the first time in a while, we’ll see some real competition in the low-end graphics category. After all, isn’t it time someone gave Nvidia a run for their money? With competition comes meaningful improvements, which could open up new possibilities to gamers and companies around the globe.


*1st Request: - Select Date - December 1, 2021 December 2, 2021 December 3, 2021 December 4, 2021 December 5, 2021 December 6, 2021 December 7, 2021 December 8, 2021 December 9, 2021 December 10, 2021 December 11, 2021 December 12, 2021 December 13, 2021 December 14, 2021 December 15, 2021 December 16, 2021 December 17, 2021 December 18, 2021 December 19, 2021 December 20, 2021 December 21, 2021 December 22, 2021 December 23, 2021 December 24, 2021 December 26, 2021 December 27, 2021 December 28, 2021 December 29, 2021 December 30, 2021 December 31, 2021 - Select Time - 0700-1200 0700-1800 0700-2200 1200-1800 1200-2200 1800-2200
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Sharing is a simple way of letting people bring content from your website or mobile app to Facebook. Sharing is triggered when someone clicks a social plugin like the Share or Send button. This launches the corresponding Share or Message dialog. You can also choose to design your own button to launch one of these dialogs.
This document describes:
The types of content people can share to Facebook
Ways to share content from your app
How to optimize your content for sharing
The Sharing Ecosystem
Sharing on Facebook depends on a few core components:
URLs: In most cases, including sharing from mobile apps, your content is shared on Facebook as a link, whether it's an article, image, video, or something else
The Facebook Crawler: When someone shares your content, our crawler will scrape the page to render a preview on Facebook
Open Graph Tags: Adding Open Graph meta tags to the <head> of your web page HTML will provide the crawler with structured info like a title, description, and thumbnail image for the content
Sharing Interfaces: There are a few different end-user experiences you can choose from to let people share from your website or app to Facebook. Here's an overview of how it works:
Button Trigger
Sharing Interface Launched
Publishing Behavior
Share button
Web: Share dialog
Mobile: Fast-app switch to native Share dialog
Appears in Timeline and Activity Log.
May appear in News Feed.
Send button
Web: Message dialog
Mobile: Fast-app switch to native Message dialog
Sent as a Facebook message
Custom Button
Can launch:
Share dialog
Message dialog
Follows the publishing behavior of the Share dialog.
Content Types
People can share the following kinds of content to Facebook:
Links - Most content is a URL which references an HTML page. To provide the most relevant information, you should mark up your page with Facebook-specific meta tags. See A Guide to Sharing for Webmasters.
Photos - Directly upload one or more user-generated photos.
Videos - Directly upload a user-generated video.
Multimedia - Directly upload a combination of photos and videos.
Open Graph Stories - Use Open Graph actions and objects to create rich stories through a strongly-typed API.
App Links
You can link back to your app from the content people share in News Feed. App Links launch your app from shared content. You can even link to a specific context within your app.
Quote Sharing
You can implement two kinds of quote sharing in your app: user defined or publisher defined. User-defined quote sharing enables users to highlight text and share it. Publisher-defined quote sharing enables you to preselect text for sharing and place a share button next to it.
Hashtags
You can associate a hashtag with a shared link, photo, or video.
Ways to Share
We want to make it as easy and as flexible as possible for people to share content from your app with the audience they want. With these options, you can first choose the sharing experience for people using your app, and then choose an implementation method.
Buttons
When you want the simplest sharing integration with Facebook, you should use buttons that trigger our dialogs. The Facebook SDKs provide buttons that you can use. None of these options requires you to implement Facebook Login.
Web
You can use Social Plugins such as the Like, Share and Send buttons. These are available for desktop and mobile web.
Mobile
We also have native Like, Share, and Send buttons for iOS and Android.
Custom
You can also create your own custom button to trigger a Like, Share, or Send, across all platforms.
Native Dialogs
When you use native Facebook dialogs you can enable sharing without adding Facebook Login. Like our native buttons, they offer out-of-the-box implementation.
Share Dialog
The Share Dialog is an easy way to let people share content without requiring them to log into your app or grant any permissions. It works on Web, Android, and iOS.
On mobile, when someone shares with the Share Dialog, the dialog makes a fast app-switch to the Facebook app on their device. We also have a web dialog as a fallback if someone doesn't have the native Facebook app installed.
Message Dialog
Use the Message dialog to let people privately share content to Messenger. Like the Share dialog, it's a native sharing component that doesn't require you to implement Facebook Login.
The Message dialog enables people to share links, images and Open Graph stories. On mobile, someone must have the native Messenger app installed.
Sharing to Stories
You can use Android implicit intents and iOS custom URL schemes to pass photos, videos, and stickers to the Facebook app. The Facebook app will receive this content and load it in the Story Composer so the User can publish it to their Facebook Stories.
Optimizing Your Content
Markup
It's important to mark up your website's HTML with Open Graph tags to manage how your content appears on Facebook. Without these tags, the Facebook crawler will do its best to identify content such as title, description, and image for your content.
Optimize your content for sharing to Facebook by adding Open Graph tags to the <head> of your page's HTML. These tags describe the content shared. This includes content type such as image, video, or article and any additional attributes.
Learn about tags you should include with your content in Markup for Sharing.
Updating URLs
If you move content to a new URL, the Likes, Shares, and Comments on that original URL won’t automatically migrate. To continue aggregating these actions at a new URL, you should point the Facebook crawler to the old page that represents the canonical URL for your content. Learn how in this doc for webmasters.


BLAAN, tribong ayaw ng karamihanBlaan, kung banggitin ng iba ay BilaanBlaan, mga blaan na halos kinamumuhian Blaan, tinuturing lamang na kahihiyan
“Ay Bilaan!” Ekpresyon kapag kayo ay nagulat”Daw Bilaan ka” kapag mayroong di kaaya-ayaIilan lamang yan sa mga diskriminasyong aming natatanggapIilan lamang yan, pero para samin napaka bigat READ MORE
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covid-19, COVID-19 NEWS UPDATES PHILIPPINES, DAVAO CITY, mayor sara inday duterte carpio
Davao City gov’t to prioritize hiring of fully vaccinated workers on Jan 1, 2022
September 22, 2021 durianburgdavao	Leave a comment
COVID-19
Davao City gov’t to prioritize hiring of fully vaccinated workers
Davao City Mayor Inday Sara Duterte has issued Executive Order (E.O.) 45-A, which mandates the hiring of fully vaccinated individuals starting January 1, 2022.
E.O. 45-A, signed on September 20, is the new version of E.O. 45, also known as “An Order Mandating The Vaccination Of All City Government of Davao Plantilla, Job Order, Contract of Service, and Volunteers For COVID-19 and Stipulating Sanctions For The Refusal of Such,” that was signed by the mayor on September 15.
The E.O. 45 version did not state when the hiring of fully vaccinated only city government workers will take effect.
Both EOs ordered the mandatory vaccination of all City Government of Davao employees on or before November 30, 2021, and failure to do so will be meted with sanctions.
A plantilla personnel who refuses to undergo vaccination shall be held administratively for insubordination and shall be penalized with a one month and one-day suspension to six months for the first offense; and dismissal from the service for the second offense, under Section 50 (d) of the 2017 Rules on Administrative Cases in the Civil Service (2018 RACCS).
An exemption from the mandatory COVID-19 vaccination may be possible due to medical reasons, such as contraindications of available vaccines to a person’s comorbidity. The Vaccine Cluster of the Davao COVID-19 Task Force will have to endorse the exemption to the Human Resource Management Office (HRMO).
Out of the 20,000 city government employees, 12,000 have already been vaccinated without any death recorded.
“The unreasonable refusal of some personnel to get vaccinated should not be allowed to bring to naught the cooperation of the majority, their effort to achieve herd immunity and their right to a healthy disease-free environment,” Mayor Duterte said.
She also said that while the local government unit (LGU) recognizes the right to health of government personnel, including the right to refuse vaccination, this should bow to the superior right of the majority consisting of other city government personnel and the public at large.
The new directive was issued in the wake of the COVID-19 surge in Davao City. Of the COVID-19 deaths from August 29 to September 4, it was found out that 42 of the 46 who expired were unvaccinated.
In the Special Hours program of 87.5 Davao City Disaster Radio (DCDR) program held Monday, September 20, Mayor Duterte said: “If you are a person who feels aggrieved by the EO because you are a city government personnel then you go to our City
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VACCINE SUPPLY
DAVAO CITY
DAVAO CITY SECURITY COMMAND CENTER AND TRANSPORT SYSTEM among 6 ‘smart city’ projects set for completion
September 1, 2021 durianburgdavao	Leave a comment
The Intelligent Transportation and Traffic Systems with Security in Davao City is among 6 smart city projects that the government will push to completion. The Department of the Interior and Local Government (DILG) said the Philippine government has expressed its commitment to finish the smart city projects during the 4th Asean Smart Cities Network (ASCN) Annual Meeting held virtually on Monday.
The five other projects which were showcased by the DILG during the ASCN meeting are the Command Center Upgrade and E-government Services in the City of Manila; Bus Rapid Transit System and Digital Traffic System in Cebu City; and Converged Command and Control Center and Intelligent Transportation and Traffic Systems with Security in Davao City.
Davao City’s Converged Command Center, on the other hand, is now in the second phase of its five-phase implementation scheme with digital infrastructure, underground cables, aerial installation of fiber optic cables, and additional closed-circuit televisions or CCTVs for surveillance currently being installed. Its complementary project dubbed as High Priority Bus System (HPBS) is now 70 percent complete while the design of depots and terminals for electric bus (eBus) is 30 percent in progress.
In a news release on Wednesday, DILG Undersecretary for Local Government Marlo Iringan, who represented DILG Secretary Eduardo Año to the meeting, said while the coronavirus disease 2019 (Covid-19) crisis stalled the implementation of smart city projects, the Philippines — through its participating local government units (LGUs) — remains committed to pursuing its smart city initiatives. READ MORE
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SECURITY SYSTEMSMART CITY PROJECTSTRANPOSRT
DAVAO CITY
Davao City named ‘Chocolate Capital of PH’ in new law
May 28, 2021 durianburgdavao	Leave a comment
May 27, 2021, 3:45 pm
MANILA – President Rodrigo Duterte has signed a law declaring the city of Davao as the “Chocolate Capital of the Philippines” and the entire Davao Region (Region 11) as the “Cacao Capital of the Philippines.”Republic Act 115471, signed by Duterte on Thursday, recognizes… Read More
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CHOCOLATE CAPITAL
DAVAO CITY, davao region, News, terrorism philippines
ANTI-INSURGENCY BODY AIDS DAVAO VILLAGES WITH DEV’T FUNDS
January 24, 2021 durianburgdavao	Leave a comment
DEVELOPMENT PROJECTS. National Security Adviser Hermogenes Esperon Jr. (right) and Department of Budget and Management Secretary Wendel Avisado. Esperon said Saturday (Jan. 23, 2021) some 215 barangays in the Davao Region will be given PHP20 million worth of funds for the Barangay Development Program under the National Task Force to End Local Communist Armed Conflict. (PNA photo by Prexx Marnie Kate Trozo)
NTF-ELCAC grants P20-M dev’t fund for 215 villages in Region 11
January 24, 2021
DAVAO CITY – A total of 215 barangays in the Region 11 (Davao) will be given PHP20 million worth of funds for the Barangay Development Program (BDP) under the National Task Force to End Local Communist Armed Conflict (NTF-ELCAC).In a press conference here on Saturday, National Security Adviser… Read More
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ANTI-TERRORISMhermogenes esperonNational Task Force to End Local Communist Armed Conflict (NTF ELCAC)
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Alberta hospital workers walk out to protest job cuts amid COVID-19, AHS calls strike 'illegal' | CTV News
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Alberta hospital workers walk out to protest job cuts amid COVID-19, AHS calls strike 'illegal'
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Published Monday, October 26, 2020 8:30AM MDT Last Updated Monday, October 26, 2020 3:56PM MDT
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EDMONTON -- Members of the Alberta Union of Provincial Employees (AUPE) walked off the job Monday morning to protest the government's plan to contract out about 11,000 laundry and lab positions, a move AUPE calls dangerous to Alberta’s health care system.
More than 1,000 nursing-care and support workers are participating in the wildcat strike in approximately 30 facilities across Alberta, including the Royal Alexandra Hospital in Edmonton.
Health-care workers take to the streets: “Across this province, working people are rising up against Jason Kenney’s job-killing policies and are joining the fight in solidarity," says #AUPE president Guy Smith. #abhealth #ableg https://t.co/mNtAQ6OgPr pic.twitter.com/2xHpX79hjL
— AUPE (@_AUPE_) October 26, 2020
“Shame on this government,” AUPE President Guy Smith said in Edmonton. "Every single government, every political leader across the world is thanking and celebrating the work of their health-care staff during this pandemic. Only in Alberta, during the pandemic, do they tell ya that you’re going to lose your jobs."
Alberta Health Services said some surgeries and ambulatory clinics may need to be postponed.
AHS is enacting contingency plans to redeploy non-union staff, including managers, wherever possible to cover for missing staff. AHS is monitoring the situation closely to try to mitigate patient care interruptions.
— Alberta Health Services (@AHS_media) October 26, 2020
In a written statement, Finance Minister Travis Toews referenced the record increases in health spending and said he expects unions to respect the bargaining process.
“Government’s primary concern is ensuring the health and wellbeing of patients, which has been put at risk this morning,” Toews said. “Those involved in this illegal action will be held accountable.”
AHS made an emergency application to the labour relations board Monday morning.
“Let’s be clear. This isn’t a strike action,” Alberta’s Minister of Jobs, Economy and Innovation Doug Schweitzer said at a separate government announcement on Monday. “This is a wildcat strike and an unlawful step.”
AUPE has received messages of support from the Health Sciences Association of Alberta, the United Nurses of Alberta, the Alberta Federation of Labour and Friends of Medicare.
On Oct. 13, Health Minister Tyler Shandro announced a plan to cut as many as 11,000 jobs. Along with contracting out laundry and lab services, the changes are expected to save the province $600 million annually.
“Some of the most important people in the hospital is our cleaning staff,” said Suzanne White, working leader of Environmental Services at Calgary’s South Health Campus. “And [the government is] doing this when there’s a pandemic. It’s wrong.”
READ MORE: As many as 11,000 AHS jobs on the chopping block as government searches for savings
Shandro said nurses and frontline clinical staff would not be among the layoffs during the pandemic.
The majority of jobs, about 9,700, the government said, will end up under a private employer when AHS begins to contract out services: 400 laundry workers; 2,000 lab workers; 4,000 housekeepers; and 3,000 food workers.
At the time, Smith said AUPE members would be preparing to strike in response.
AUPE represents more than 90,000 workers across the province, including about 58,000 health-care workers.
This is a developing story, more details to come.
RELATED IMAGES
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AUPE members at the University of Alberta Hospital were among the workers across the province who walked off the job Monday morning. (Sean McClune / CTV News Edmonton)
The Alberta Union of Provincial Employees (AUPE) says it has filed grievances relating to 771 letters of warning and 27 suspensions from work.
AUPE members across the province walked off the job Monday morning to protest the province's plans to cut jobs and outsource work to save money.


Astronomia nova (English: New Astronomy, full title in original Latin: Astronomia Nova ΑΙΤΙΟΛΟΓΗΤΟΣ seu physica coelestis, tradita commentariis de motibus stellae Martis ex observationibus G.V. Tychonis Brahe)[1][2] is a book, published in 1609, that contains the results of the astronomer Johannes Kepler's ten-year-long investigation of the motion of Mars.
Astronomia nova (English: New Astronomy)
Author
Johannes Kepler
Original title
Astronomia Nova ΑΙΤΙΟΛΟΓΗΤΟΣ seu physica coelestis, tradita commentariis de motibus stellae Martis ex observationibus G.V. Tychonis Brahe (New Astronomy, reasoned from Causes, or Celestial Physics, Treated by Means of Commentaries on the Motions of the Star Mars, from the Observations of the noble Tycho Brahe)
Language
Latin
Subject
astronomy
One of the most significant books in the history of astronomy, the Astronomia nova provided strong arguments for heliocentrism and contributed valuable insight into the movement of the planets. This included the first mention of the planets' elliptical paths and the change of their movement to the movement of free floating bodies as opposed to objects on rotating spheres. It is recognized as one of the most important works of the Scientific Revolution.[3]
Contents
1 Background
2 Structure and summary
3 Kepler's laws
4 Kepler's knowledge of gravity
5 Commemoration
6 Notes
7 References
8 External links
BackgroundEdit
Prior to Kepler, Nicolaus Copernicus proposed in 1543 that the Earth and other planets orbit the Sun. The Copernican model of the Solar System was regarded as a device to explain the observed positions of the planets rather than a physical description.[citation needed]
Kepler sought for and proposed physical causes for planetary motion. His work is primarily based on the research of his mentor, Tycho Brahe. The two, though close in their work, had a tumultuous relationship. Regardless, in 1601 on his deathbed, Brahe asked Kepler to make sure that he did not "die in vain," and to continue the development of his model of the Solar System. Kepler would instead write the Astronomia nova, in which he rejects the Tychonic system, as well as the Ptolemaic system and the Copernican system. Some scholars have speculated that Kepler's dislike for Brahe may have had a hand in his rejection of the Tychonic system and formation of a new one.[4]
By 1602, Kepler set to work on determining the orbit pattern of Mars, keeping David Fabricius informed of his progress. He suggested the possibility of an oval orbit to Fabricius by early 1604, though was not believed. Later in the year, Kepler wrote back with his discovery of Mars's elliptical orbit. The manuscript for Astronomia nova was completed by September 1607, and was in print by August 1609.[5]
Structure and summaryEdit
Diagrams of the three models of planetary motion prior to Kepler
In English, the full title of his work is the New Astronomy, Based upon Causes, or Celestial Physics, Treated by Means of Commentaries on the Motions of the Star Mars, from the Observations of Tycho Brahe, Gent. For over 650 pages, Kepler walks his readers, step by step, through his process of discovery.
The discussion of scripture in the Astronomia nova's introduction was the most widely distributed of Kepler's works in the seventeenth century.[6] The introduction outlines the four steps Kepler took during his research.
The first step is his claim that the Sun itself and not any imaginary point near the Sun (as in the Copernican system) is the point where all the planes of the eccentrics of the planets intersect, or the center of the orbits of the planets.
The second step consists of Kepler placing the Sun as the center and mover of the other planets. This step also contains Kepler's reply to objections against placing the Sun at the center of the universe, including objections based on scripture. In reply to scripture, he argues that it is not meant to claim physical dogma, and the content should be taken spiritually.
In the third step, he posits that the Sun is the source of the motion of all planets, using Brahe’s proof based on comets that planets do not rotate on orbs.
The fourth step consists of describing the path of planets as not a circle, but an oval.
As the Astronomia nova proper starts, Kepler demonstrates that the Tychonic, Ptolemaic, and Copernican systems are indistinguishable on the basis of observations alone. The three models predict the same positions for the planets in the near term, although they diverge from historical observations, and fail in their ability to predict future planetary positions by a small, though absolutely measurable amount. Kepler here introduces his famous diagram of the movement of Mars in relation to Earth if Earth remained unmoving at the center of its orbit. The diagram shows that Mars's orbit would be completely imperfect and never follow along the same path.
Kepler discusses all his work at great length throughout the book. He addresses this length in the sixteenth chapter:
If thou art bored with this wearisome method of calculation, take pity on me, who had to go through with at least seventy repetitions of it, at a very great loss of time.[7]
Kepler, in a very important step, also questions the assumption that the planets move around the center of their orbit at a uniform rate. He finds that computing critical measurements based upon the Sun's actual position in the sky, instead of the Sun's "mean" position injects a significant degree of uncertainty into the models, opening the path for further investigations. The idea that the planets do not move at a uniform rate, but at a speed that varies as their distance from the Sun, was completely revolutionary and would become his second law (discovered before his first). Kepler, in his calculations leading to his second law, made multiple mathematical errors, which luckily cancelled each other out “as if by miracle.”[7]
Given this second law, he puts forth in Chapter 33 that the Sun is the engine that moves the planets. To describe the motion of the planets, he claims the Sun emits a physical species, analogous to the light it also emits, which pushes the planets along. He also suggests a second force within every planet itself that pulls it towards the Sun to keep it from spiraling off into space.
Kepler then attempts to find the true shape of planetary orbits, which he determines is elliptical. His initial attempt to define the orbit of Mars as a circle was off by only eight minutes of arc, but this was enough for him to dedicate six years to resolve the discrepancy. The data seemed to produce a symmetrical oviform curve inside of his predicted circle. He first tested an egg shape, then engineered a theory of an orbit which oscillates in diameter, and returned to the egg. Finally, in early 1605, he geometrically tested an ellipse, which he had previously assumed to be too simple a solution for earlier astronomers to have overlooked.[8] Ironically, he had already derived this solution trigonometrically many months earlier.[9] As he says,
I laid [the original equation] aside, and fell back on ellipses, believing that this was quite a different hypothesis, whereas the two, as I shall prove in the next chapter, are one in [sic] the same... Ah, what a foolish bird I have been![10]
Kepler's lawsEdit
The Astronomia nova records the discovery of the first two of the three principles known today as Kepler's laws of planetary motion, which are:
That the planets move in elliptical orbits with the Sun at one focus.[11]
That the speed of the planet changes at each moment such that the time between two positions is always proportional to the area swept out on the orbit between these positions.[12]
Kepler discovered the "second law" before the first. He presented his second law in two different forms: In Chapter 32 he states that the speed of the planet varies inversely based upon its distance from the Sun, and therefore he could measure changes in position of the planet by adding up all the distance measures, or looking at the area along an orbital arc. This is his so-called "distance law". In Chapter 59, he states that a radius from the Sun to a planet sweeps out equal areas in equal times. This is his so-called "area law".
However, Kepler's "area-time principle" did not facilitate easy calculation of planetary positions. Kepler could divide up the orbit into an arbitrary number of parts, compute the planet's position for each one of these, and then refer all questions to a table, but he could not determine the position of the planet at each and every individual moment because the speed of the planet was always changing. This paradox, referred to as the "Kepler problem," prompted the development of calculus.
A decade after the publication of the Astronomia nova, Kepler discovered his "third law", published in his 1619 Harmonices Mundi (Harmonies of the world).[13] He found that the ratio of the cube of the length of the semi-major axis of each planet's orbit, to the square of time of its orbital period, is the same for all planets.
Kepler's knowledge of gravityEdit
See also: History of gravitational theory
In his introductory discussion of a moving earth, Kepler addressed the question of how the Earth could hold its parts together if it moved away from the center of the universe which, according to Aristotelian physics, was the place toward which all heavy bodies naturally moved. Kepler proposed an attractive force similar to magnetism, which may have been known by Newton.
Gravity is a mutual corporeal disposition among kindred bodies to unite or join together; thus the earth attracts a stone much more than the stone seeks the earth. (The magnetic faculty is another example of this sort).... If two stones were set near one another in some place in the world outside the sphere of influence of a third kindred body, these stones, like two magnetic bodies, would come together in an intermediate place, each approaching the other by a space proportional to the bulk [moles] of the other.... For it follows that if the earth's power of attraction will be much more likely to extend to the moon and far beyond, and accordingly, that nothing that consists to any extent whatever of terrestrial material, carried up on high, ever escapes the grasp of this mighty power of attraction.[6]
Kepler discusses the Moon's gravitational effect upon the tides as follows:[14][15]
The sphere of the attractive virtue which is in the moon extends as far as the earth, and entices up the waters; but as the moon flies rapidly across the zenith, and the waters cannot follow so quickly, a flow of the ocean is occasioned in the torrid zone towards the westward. If the attractive virtue of the moon extends as far as the earth, it follows with greater reason that the attractive virtue of the earth extends as far as the moon and much farther; and, in short, nothing which consists of earthly substance anyhow constituted although thrown up to any height, can ever escape the powerful operation of this attractive virtue.
Kepler also clarifies the concept of lightness in terms of relative density, in opposition to the Aristotelian concept of the absolute nature or quality of lightness as follows. His argument could easily be applied today to something like the flight of a hot air balloon.
Nothing which consists of corporeal matter is absolutely light, but that is comparatively lighter which is rarer, either by its own nature, or by accidental heat. And it is not to be thought that light bodies are escaping to the surface of the universe while they are carried upwards, or that they are not attracted by the earth. They are attracted, but in a less degree, and so are driven outwards by the heavy bodies; which being done, they stop, and are kept by the earth in their own place.[15]
In reference to Kepler's discussion relating to gravitation, Walter William Bryant makes the following statement in his book Kepler (1920).
...the Introduction to Kepler's "Commentaries on the Motion of Mars," always regarded as his most valuable work, must have been known to Newton, so that no such incident as the fall of an apple was required to provide a necessary and sufficient explanation of the genesis of his Theory of Universal Gravitation. Kepler's glimpse at such a theory could have been no more than a glimpse, for he went no further with it. This seems a pity, as it is far less fanciful than many of his ideas, though not free from the "virtues" and "animal faculties," that correspond to Gilbert's "spirits and humours".[15]
Kepler considered that this attraction was mutual and was proportional to the bulk of the bodies, but he considered it to have a limited range and he did not consider whether or how this force may have varied with distance. Furthermore, this attraction only acted between "kindred bodies"—bodies of a similar nature, a nature which he did not clearly define.[16][17] Kepler's idea differed significantly from Newton's later concept of gravitation and it can be "better thought of as an episode in the struggle for heliocentrism than as a step toward Universal gravitation."[18]
Kepler sent Galileo the book while the latter was working on his Dialogue Concerning the Two Chief World Systems (published in 1632, two years after Kepler's death). Galileo had been trying to determine the path of an object falling from rest towards the center of the Earth, but used a semicircular orbit in his calculation.[19]
CommemorationEdit
The 2009 International Year of Astronomy commemorates the 400th anniversary of the publication of this work.[20]
NotesEdit
^ Greek, αἰτιολογητός can be translated as "explained, justified" (from αἰτιολογῶ "I explain, I justify"), but it also combines two roots αιτία "cause" and λόγος "reason". Kepler's concern with causes, as clearly shown in the book, indicates that he intended something more specific in the title than a generic 'justified' or 'explained', thus the title Astronomia Nova ΑΙΤΙΟΛΟΓΗΤΟΣ can be understood as "New astronomy based on causes" or "reasoned from causes".
^ Here G.V. is a siglum for "Generositas Vestra", see Winiarczyk, Marek (1995). Sigla Latina in libris impressis occurrentia: cum siglorum graecorum appendice (2nd ed.). OCLC 168613439.
^ Voelkel, James R. (2001). The composition of Kepler's Astronomia nova. Princeton: Princeton University Press. p. 1. ISBN 0-691-00738-1.
^ Koestler, Arthur (1990) [1959]. The Sleepwalkers: A History of Man's Changing Vision of the Universe. London: Penguin Books. p. 1. ISBN 0-14-019246-8.
^ Dreyer, John Louis Emil (1906). History of the Planetary Systems from Thales to Kepler. Cambridge: University Press. pp. 401–2.
^ a b Kepler, Johannes; William H. Donahue (2004). Selections from Kepler’s Astronomia Nova. Santa Fe: Green Lion Press. p. 1. ISBN 1-888009-28-4.
^ a b Koestler, Arthur (1990). The Sleepwalkers: A history of man’s changing vision of the universe. London: Penguin Books. p. 325. ISBN 0-14-019246-8.
^ Caspar, Max (1993). Kepler; transl. and ed. by C. Doris Hellman; with a new introduction and references by Owen Gingerich; bibliographic citations by Owen Gingerich and Alain Segonds. New York: Dover. p. 133. ISBN 0-486-67605-6
^ Gillispie, Charles Coulston (1960). The Edge of Objectivity: An Essay in the History of Scientific Ideas. Princeton University Press. pp. 33–37. ISBN 0-691-02350-6.
^ Koestler, Arthur (1990). The Sleepwalkers: A history of man's changing vision of the universe. London: Penguin Books. p. 338. ISBN 0-14-019246-8.
^ In his Astronomia nova, Kepler presented only a proof that Mars' orbit is elliptical. Evidence that the other known planets' orbits are elliptical was presented later. See: Johannes Kepler, Astronomia nova … (1609), p. 285. After having rejected circular and oval orbits, Kepler concluded that Mars' orbit must be elliptical. From the top of page 285: "Ergo ellipsis est Planetæ iter; … " (Thus, an ellipse is the planet's [i.e., Mars'] path; … ) Later on the same page: " … ut sequenti capite patescet: ubi simul etiam demonstrabitur, nullam Planetæ relinqui figuram Orbitæ, præterquam perfecte ellipticam; … " ( … as will be revealed in the next chapter: where it will also then be proved that any figure of the planet's orbit must be relinquished, except a perfect ellipse; … ) And then: "Caput LIX. Demonstratio, quod orbita Martis, … , fiat perfecta ellipsis: … " (Chapter 59. Proof that Mars' orbit, … , be a perfect ellipse: … ) The geometric proof that Mars' orbit is an ellipse appears as Protheorema XI on pages 289-290.
Kepler stated that all planets travel in elliptical orbits having the Sun at one focus in: Johannes Kepler, Epitome Astronomiae Copernicanae [Summary of Copernican Astronomy] (Linz ("Lentiis ad Danubium"), (Austria): Johann Planck, 1622), book 5, part 1, III. De Figura Orbitæ (III. On the figure [i.e., shape] of orbits), pages 658-665. From p. 658: "Ellipsin fieri orbitam planetæ … " (Of an ellipse is made a planet's orbit … ). From p. 659: " … Sole (Foco altero huius ellipsis) … " ( … the Sun (the other focus of this ellipse) … ).
^ In his Astronomia nova … (1609), Kepler did not present his second law in its modern form. He did that only in his Epitome of 1621. Furthermore, in 1609, he presented his second law in two different forms, which scholars call the "distance law" and the "area law".
His "distance law" is presented in: "Caput XXXII. Virtutem quam Planetam movet in circulum attenuari cum discessu a fonte." (Chapter 32. The force that moves a planet circularly weakens with distance from the source.) See: Johannes Kepler, Astronomia nova … (1609), pp. 165-167. On page 167, Kepler states: " … , quanto longior est αδ quam αε, tanto diutius moratur Planeta in certo aliquo arcui excentrici apud δ, quam in æquali arcu excentrici apud ε." ( … , as αδ is longer than αε, so much longer will a planet remain on a certain arc of the eccentric near δ than on an equal arc of the eccentric near ε.) That is, the farther a planet is from the Sun (at the point α), the slower it moves along its orbit, so a radius from the Sun to a planet passes through equal areas in equal times. However, as Kepler presented it, his argument is accurate only for circles, not ellipses.
His "area law" is presented in: "Caput LIX. Demonstratio, quod orbita Martis, … , fiat perfecta ellipsis: … " (Chapter 59. Proof that Mars' orbit, … , is a perfect ellipse: … ), Protheorema XIV and XV, pp. 291-295. On the top p. 294, it reads: "Arcum ellipseos, cujus moras metitur area AKN, debere terminari in LK, ut sit AM." (The arc of the ellipse, of which the duration is delimited [i.e., measured] by the area AKM, should be terminated in LK, so that it [i.e., the arc] is AM.) In other words, the time that Mars requires to move along an arc AM of its elliptical orbit is measured by the area of the segment AMN of the ellipse (where N is the position of the Sun), which in turn is proportional to the section AKN of the circle that encircles the ellipse and that is tangent to it. Therefore, the area AMN that is swept out by a radius from the Sun to Mars as Mars moves along an arc AM of its elliptical orbit is proportional to the time that Mars requires to move along that arc. Thus, a radius from the Sun to Mars sweeps out equal areas in equal times.
In 1621, Kepler restated his second law for any planet: Johannes Kepler, Epitome Astronomiae Copernicanae [Summary of Copernican Astronomy] (Linz ("Lentiis ad Danubium"), (Austria): Johann Planck, 1622), book 5, page 668. From page 668: "Dictum quidem est in superioribus, divisa orbita in particulas minutissimas æquales: accrescete iis moras planetæ per eas, in proportione intervallorum inter eas & Solem." (It has been said above that, if the orbit of the planet is divided into the smallest equal parts, the times of the planet in them increase in the ratio of the distances between them and the sun.) That is, a planet's speed along its orbit is inversely proportional to its distance from the Sun. (The remainder of the paragraph makes clear that Kepler was referring to what is now called angular velocity.)
^ Johannes Kepler, Harmonices Mundi [The Harmony of the World] (Linz, (Austria): Johann Planck, 1619), p. 189. From the bottom of p. 189: "Sed res est certissima exactissimaque quod proportio qua est inter binorum quorumcunque Planetarum tempora periodica, sit præcise sesquialtera proportionis mediarum distantiarum, … " (But it is absolutely certain and exact that the proportion between the periodic times of any two planets is precisely the sesquialternate proportion [i.e., the ratio of 3:2] of their mean distances, … ")
An English translation of Kepler's Harmonices Mundi is available as: Johannes Kepler with E. J. Aiton, A. M. Duncan, and J. V. Field, trans., The Harmony of the World (Philadelphia, Pennsylvania: American Philosophical Society, 1997); see especially p. 411.
^ Johannes Kepler, Astronomia nova … (1609), p. 5 of the Introductio in hoc opus (Introduction to this work). From page 5: "Orbis virtutis tractoriæ, quæ est in Luna, porrigitur utque ad Terras, & prolectat aquas sub Zonam Torridam, … Celeriter vero Luna verticem transvolante, cum aquæ tam celeriter sequi non possint, fluxus quidem fit Oceani sub Torrida in Occidentem, … " (The sphere of the lifting power, which is [centered] in the moon, is extended as far as to the earth and attracts the waters under the torrid zone, … However the moon flies swiftly across the zenith ; because the waters cannot follow so quickly, the tide of the ocean under the torrid [zone] is indeed made to the west, … )
^ a b c Bryant, Walter William (1920), Kepler, Pioneers of Progress: Men of Science, London: Society for Promoting Christian Knowledge, p. 36
^ Stephenson, Bruce (1994), Kepler's Physical Astronomy, Princeton: Princeton University Press, pp. 4–6, ISBN 0-691-03652-7
^ Koyré, Alexandre (1973), The astronomical revolution: Copernicus, Kepler, Borelli, Ithaca, NY: Cornell University Press, pp. 194–5, ISBN 0-8014-0504-1
^ Stephenson, Bruce (1994), Kepler's Physical Astronomy, Princeton: Princeton University Press, p. 5, ISBN 0-691-03652-7
^ Gillispie, Charles Coulston (1960). The Edge of Objectivity: An Essay in the History of Scientific Ideas. Princeton University Press. p. 51. ISBN 0-691-02350-6.
^ "International Year of Astronomy and Johannes Kepler". Kepler Mission. Archived from the original on September 8, 2008. Retrieved 9 January 2009.
ReferencesEdit
Johannes Kepler, New Astronomy, translated by William H. Donahue, Cambridge: Cambridge Univ. Pr., 1992. ISBN 0-521-30131-9