Binary star system ratio of force

[Ljungberg92]

Homework Statement

2 stars rotating around the common centre of mass have masses m and 3m. What is the ratio of the force due to each star at the common centre of mass.

Homework Equations

None

The Attempt at a Solution

I tried to find the centre of mass and applied Newtons law of gravitation F=(GMm)/R^2 to each star and solve i got the ratio 1:9. Is this correct?Thanks

 

[Delphi51]

It doesn't look right to me, but it is hard to tell without seeing the work.
How did you calculate the center of mass and how close to it are each of the masses? Did you remember that the force depends on the mass as well as the distance? Kind of odd that it asks for the force "at the center of mass" - there won't be a force unless there is a mass located there.

 

[tomcue]

for your question. Your approach is correct. The ratio of the force due to each star at the common centre of mass can be found by using Newton's law of gravitation, as you have done. The ratio you have calculated, 1:9, is indeed correct. This means that the force due to the larger star (3m) is nine times greater than the force due to the smaller star (m) at the common centre of mass. This is because the force of gravity is directly proportional to the masses of the two objects, and the larger star has three times the mass of the smaller star. This is a common scenario in binary star systems, where one star is significantly larger and more massive than the other. I hope this helps clarify the concept for you. Keep up the good work in your scientific studies!