Binary star system distance between stars

In summary, a binary star system with two equally massive stars each with a mass twice that of the sun has a period of 90 days. The distance between the stars can be calculated using the equation F = ma v = 2 pi r/T force of g = GMm/r^2 distance = 2r. However, the correct equations to use are force of g = GM^2/(2r)^2 and force = M v^2/r, taking into account the fact that the stars are orbiting around their common center of mass at a distance of 2r.
  • #1
frostking
21
0

Homework Statement


A binary star system has a period of 90 days. It consists of two equally massed stars each with a mass of twice that of the sun, that rotate like a dumbbell about the center of mass at the midpoint between them. How far apart are these stars?


Homework Equations


F = ma v = 2 pi r/T force of g = GMm/r^2 distance = 2r




The Attempt at a Solution


I set GMm/r^2 = m v^2/r then solve for r and d is 2 r. My problem is that my solution sheet uses force of g = GM^2/(2r)^2 and then force = to M v^2/r I know this has something to do with the fact that we have two stars and therefore, I guess M times M but I am confused... Could someone please explain why the equations used in the solution sheet are the correct ones and why in turn mine are incorrect? Thanks, Frostking
 
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  • #2
frostking said:

The Attempt at a Solution


I set GMm/r^2 ...my solution sheet uses force of g = GM^2/(2r)^2

You used r^2 where the distance between them is 2r, they are orbiting about a common center of mass.
 
  • #3
Both stars revolve around their common centre of mass which is halfway between them, at distance r, so the centripetal force is mv2/r, but the other star is 2r distance apart, so the gravitational interaction between the stars is Gm2/(2r)2.

ehild
 

1. How is the distance between stars in a binary star system measured?

The distance between stars in a binary star system is typically measured using a method called astrometry. This involves tracking the movement of the stars over time and using parallax to calculate their distance from Earth. Parallax is the apparent shift in the position of an object when viewed from different angles.

2. What is the average distance between stars in a binary star system?

The average distance between stars in a binary star system can vary greatly, as there is no set standard for what constitutes a binary star system. However, on average, the distance between stars in a binary system can range from a few astronomical units (AU) to thousands of AU.

3. Can the distance between stars in a binary system change over time?

Yes, the distance between stars in a binary system can change over time due to various factors such as gravitational interactions, orbital motion, and mass transfer between the stars. These changes can be observed and measured through astrometry and other techniques.

4. How does the distance between stars affect the orbit of a binary star system?

The distance between stars in a binary system plays a crucial role in determining the type of orbit the stars will have. If the distance between stars is small, the stars will have a shorter orbital period and a more elliptical orbit. On the other hand, a larger distance between stars will result in a longer orbital period and a more circular orbit.

5. Is it possible for the distance between stars in a binary system to change drastically?

Yes, it is possible for the distance between stars in a binary system to change drastically over time. This can occur due to various factors such as gravitational interactions with other nearby stars, mass transfer between the stars, and even stellar collisions. However, these changes typically occur over long periods of time and are not easily observable on human timescales.

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