Two planets with identical mass are orbiting a distant star at the same speed. Planet X is twice as far from?

Two planets with identical mass are orbiting a distant star at the same speed. Planet X is twice as far from the star as Planet Y. How will the force the star exerts on Planet Y compare to the force the star exerts on Planet X?Two planets with identical mass are orbiting a distant star at the same speed. Planet X is twice as far from?The net force on each planet:

F = mv^2/r

v = sqrt(rF/m)



For planet X:

v = sqrt[(2r)(FX)/m] [1]



For planet Y (mass and speed are the same as planet X):

v = sqrt[(r)(FY)/m] [2]



[1] = [2]:

sqrt[(2r)(FX)/m] = sqrt[(r)(FY)/m]

2(FX) = (FY)



Because this answer is inconsistent with the dynamics approach (inverse square law due to gravity), this problem describes an unrealistic scenario... Either the gravitational forces on these planets don't follow an inverse square law (to have the same speed under the other conditions given) or (more likely) the creator if this problem gave too much (erroneous) information in the problem (the planets won't have the same speed acting under gravity at the distances given).Two planets with identical mass are orbiting a distant star at the same speed. Planet X is twice as far from?The force on Y is greater than on X.

The gravitational force is given by Newtons Law of Gravitation:

F = G Mm / r^2

Because X is farther away r must be bigger. and when you divide by a larger number the result is smaller



This is one of many forces in physics that respects a 1/r^2 relation, the force is inversely proportional to the square of the distance.



So more specifically:

G, M, and m are all the same values for both planets.

G is a constant, and M is the mass of the star, m is the mass of the planet, since planets X and Y have similar mass then m is the same value in both situations.



So the only difference in the two situations is r. Let's say that R is the distance from planet Y to the star so we have the force given by:

Fy = G Mm / R^2

Now, the distance to X is 2R because it's twice as far, so we have:

Fx = G Mm / (2R)^2



you can take the 2 out to the front to get the form:

Fx = (1/4) G Mm / R^2

everything after the (1/4) is the same as Fy right?

So

Fx = (1/4) Fy



This shows that the force on planet X is one fourth as great as the force on planet Y.