Using Kepler's laws to find out various things about binary star systems

[QuantumPerihelion]

I'm really not getting Kepler's laws, so I have four different questions about how binary star systems work.

 

First, say there is a binary system that consists of two white dwarfs in circular orbits with an orbital period of 60 days. Is it even possible yo find the maximum distance between the two white dwarfs?

 

 

Next, If one of the white dwarfs is twice as massive as the other, what is the approximate maximum orbital radius of the smaller star?

 

 

Next, If the angular separation of the two white dwarfs is measured (I don't know how) to be 0.013 arcseconds(the system is viewed face-on). If the stars were estimated to have equal masses of 0.8 M_Sun each, approximately how far away would the system be?

 

 

Lastly, if the mass ratio of the two white dwarfs were 3:1 and the distance between them were 0.15 AU, what would be the approximate radius of the more massive star's orbit?

 

Not sure if this should go to homework help because it's just some problems I got from the internet, but any help would be greatly appreciated.

[Country Boy]

Well, what are Kepler's laws?

[QuantumPerihelion]

Well, what are Kepler's laws?

http://www.physicsclassroom.com/class/circles/Lesson-4/Kepler-s-Three-Laws

[J.C.MacSwell]

Aren't Keplers Laws based on something relatively small orbiting something significantly larger? (specifically the planets around the Sun in our solar system)

 

Edit: I guess it does work for binaries also...thanks Mordred

Edited January 25, 2017 by J.C.MacSwell

[Mordred]

No it works for all orbitting bodies but only predominantly two body systems for good accuracy. Accuracy gets Elusive on three or more bodies. At least his laws do.

Edited January 25, 2017 by Mordred

[Janus]

I'm really not getting Kepler's laws, so I have four different questions about how binary star systems work.

 

First, say there is a binary system that consists of two white dwarfs in circular orbits with an orbital period of 60 days. Is it even possible yo find the maximum distance between the two white dwarfs?

Yes, if you know the sum of the masses for the two stars.

Next, If one of the white dwarfs is twice as massive as the other, what is the approximate maximum orbital radius of the smaller star?

1. [math]r = D \frac{M+m}{m}[/math]

 

where r is the orbital radius of the smaller star, D is the distance between the star's centers, M the mass of the larger star, and m the mass of the smaller star.

Next, If the angular separation of the two white dwarfs is measured (I don't know how) to be 0.013 arcseconds(the system is viewed face-on). If the stars were estimated to have equal masses of 0.8 M_Sun each, approximately how far away would the system be?

Use the formula

 

2. [math]T = 2 \pi \sqrt{\frac{D^3}{G(M+m)}}[/math]

 

to solve for D, then use trig to solve for the distance to the pair.

Note that the equation is a form of Kepler's third law that allows you to assign actual values to D or T(the orbit period) if you know other and the mass of the stars.

 

Lastly, if the mass ratio of the two white dwarfs were 3:1 and the distance between them were 0.15 AU, what would be the approximate radius of the more massive star's orbit?

You can use equations 1 and 2 as long as you know either the mass of one of the stars or the sum of the masses of the two stars.

Not sure if this should go to homework help because it's just some problems I got from the internet, but any help would be greatly appreciated.

Edited January 25, 2017 by Janus