Sun's gravitational pull problem

AI Thread Summary
To determine the distance from Pluto where a space probe experiences balanced gravitational forces from both the Sun and Pluto, the gravitational force equations must be set equal. The mass of Pluto is approximately 1.3e22 kg, and the mass of the Sun is about 1.99e30 kg. By applying the gravitational force formula, the relationship between the distances to the Sun and Pluto can be established. The correct approach involves cancelling constants and solving for the ratio of distances, leading to the calculation of the probe's position. Accurate calculations are crucial for finding the correct distance, which is initially miscalculated as 4.8e8 km.
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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?
 
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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.
 

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