Calculating the Mass Ratio of Orbiting Stars Using Gravitational Fields

[breeno]

First of all, I'm new to this forum, it's good to be here! I've been studying for my next physics exam and am having trouble with one type of question, here it is (I have tried my best to replicate the image on paint):

Homework Statement

Two stars of masses "M" and "m" are in orbit around each other. As shown in the following diagram, they are a distance "R" apart. A Spacecraft located at point X experiences zero net gravitational force from these stars. Calculate the ratio of M/m.

Homework Equations

G=(GM/R²)

Fg = (GMm/R²) = mg

Where G is the gravitation constant which is 6.67 x 10^-11
R = Radius
M = Mass
m = Mass
Fg = Gravitational force
g = gravitational field strength

The Attempt at a Solution

We know that at point X, Fg is 0. I tried plugging a whole bunch of numbers in, but I can't find a question similar and am struggling with the process of it. I'm pretty sure we use the second equation, but I seem to be screwing up the arithmetic.

Any help would be appreciated!

 

[cgi093]

Well, since the net force = 0, and they are opposing, we know that Fg1 = Fg2. Thus, GMfirststarMspaceship/0.8^2 = GMsecondstarMspaceship/0.2^2. G and the mass of the spaceship can be divided out of the equation, leaving us with Mstar1/0.8^2 = Mstar2/0.2^2. Thus, Mstar1/Mstar2 = 0.8^2/0.2^2. So Mstar1/Mstar2 = 16.

Just realized I messed with your variables a bit. Just to make it clear, Mfirststar = M and Msecondstar = m. Hope that helps.

 

[breeno]

Thankyou so much, I've been struggling with that and you've made it much clearer than my book ever would have, much appreciated!