This is a challenging multi-step problem. Solve it on paper, writing out each st

Question

This is a challenging multi-step problem. Solve it on paper, writing out each step carefully. When doing calculations, do not round intermediate values. Note: If you have approached the problem in a principled way, do not abandon your approach if your numerical answer is not accepted; check your calculations! This problem is closely related to the spectacular impact of the comet Shoemaker-Levy with Jupiter in July 1994. (More information about the event can be found here.) A rock far outside a solar system similar to ours is initially moving very slowly relative to its sun, in the plane of the orbit of a large planet (about the size of Jupiter) around its sun. The rock falls toward the sun, but on its way to the sun it collides with the planet. The mass of the planet is 7.0 x 10^27 kg, the mass of its sun is 2.7 x 10 kg, the radius of the planet is 1.5 x 10^8 m, and the center-to-center distance from the planet to the sun is 8.5 x 10^11 m. Calculate the rock?s speed just before it collides with the planet. Which of these assumptions or approximations did you make in your analysis? (Select all that apply.) The speed of the planet did not change significantly. The distance between the planet and the star did not change significantly. U The initial speed of the rock was nearly zero. U The interaction of the rock and the sun was not significant. The speed of the sun did not change significantly. The speed of the rock did not change significantly.

Explanation / Answer

Assuming the potential energy due to gravity of the rock sun ans rock planet system is 0 when it is outside the solar system.

Conserving energy,

-GmMs/r1-GmMp/r2+0.5mv^2=0

G(Ms/r1+Mp/r2)=0.5v^2

v=sqrt(2G(Ms/r1+Mp/r2))=sqrt(2*6.673*10^-11*(2.7*10^30/(8.5*10^11)+7*10^27/(1.5*10^8)))=81560m/s

b)All the assumptions apply apart from these 2:

The interaction of the rock and the sun was not significant.

the speed of the rock did not change significantly.

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