Sun's gravitational pull problem

[jperk980]

How far from Pluto must a space probe be along a line toward the Sun so that the Sun's gravitational pull on the probe balances Pluto's pull?

I know that Fs=Fsp and that when i elminate terms i get ((Rsp-x)/x)^2=(Ms/Mp) i uncderstand the mass of pluto to be 1.3e22 kg and the mass of the sun to be 1.99e30 kg and the radius to be 5.91e15 m. I get 4.8e8 to be my answer in km. That is not correct however. Can you help me?

 

[mgb_phys]

The force of gravity is F = G M m / r^2
So simply set Msun / dsun^2 = Mpluto / dpluto^2, Cancelling G and the mass of you.
Then you can work out a ratio between dsun and dpluto. You know dsun / dpluto so you can work out the position.

 

[ogb p]

Based on the given information, I believe your calculation is incorrect. The distance at which the Sun's gravitational pull on the probe balances Pluto's pull is known as the "Roche limit" and can be calculated using the formula R = 2.44 * (Rp*(Mp/Ms)^(1/3)), where R is the distance from Pluto, Rp is Pluto's radius, Mp is Pluto's mass, and Ms is the Sun's mass.

Using the values given, the Roche limit for Pluto is approximately 17,000 km. This means that the space probe would need to be at least 17,000 km away from Pluto along a line towards the Sun in order for the two gravitational pulls to balance each other out. This distance may vary slightly depending on the exact masses and radii used in the calculation.

I hope this helps clarify the concept and calculation for you. If you are still having trouble, I suggest seeking assistance from a teacher or fellow scientist.