Hello can you help me solve the prompt? It will require knowing how to calculate the center of mass, the velocity of center of mass, and researching general space assumptions. All necessary references can be found below, but it may require some additional research.

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Example Problem 1.6 (for reference): Center of Mass of the Earth-Moon System Using data from text appendix, determine how far the center of mass of the Earth-moon system is from the center of Earth. Compare this distance to the radius of Earth, and comment on the result. Ignore the other objects in the solar system. Strategy We get the masses and separation distance of the Earth and moon, impose a coordinate system, and use Equation 9.29 with just / = 2 objects. We use a subscript "e" to refer to Earth, and subscript "m" to refer to the moon. Solution Define the origin of the coordinate system as the center of Earth. Then, with just two objects, Equation 9.29 becomes R = " mere + mmm me + mm From Appendix D, me = 5.97 x 10"* kg mm = 7.36 x 10"2 kg I'm = 3.82 x 10% m. We defined the center of Earth as the origin, so re = 0 m. Inserting these into the equation for R gives R = (5.97 x 1024 kg)(0 m)+(7.36 x 1022 kg) (3.82 x 108 m) 5.97 x 1024 kg+7.36 x 1022 kg = 4.64 x 100 m. Significance The radius of Earth is 6.37 x 10 m, so the center of mass of the Earth-moon system is (6.37 - 4.64) x 105 m = 1.73 x 100 m = 1730 km (roughly 1080 miles) below the surface of Earth. The location of the center of mass is shown (not to scale). RCMSearching for exoplanets It might look like the Sun stays still as the planets orbit even neglecting the Sun's motion around the Milky Way Galaxy but it actually wobbles. it (a) (19) From the vantage point of Jupiter, the Sun looks to be stationary as we orbit it. Fi'om the reference frame of the center of mass (the barycenter). the Sun and Jupiter orbit around the barycenter. In the center-of-mass reference frame, nd the \"orbital" velocity of the Sun. When we view stars from far away, we usually can't see the planets, but we can see the star wobble around the baryeenter. The most sophisticated telescopes and spectrographs have detected this wobbling of stars (called "radial velocities") as low as about 70 cm/s. Think about that. We can detect a star 70 light-years away that is wobbling at an ant's speed! In this case, the period is about 7 days, so we can watch it very closely. Would our instruments be able to detect the wobble of the Sun induced by Jupiter if we viewed it from outside the Solar System? Optional: could we detect the wobble of the Sun by the Earth