#5 please For non-solid systems, the force of gravity determines orbital motion. We know that thestrength of gravity depends on mass and distance. Therefore, we can learn about the massdistribution (how much mass is located in a given area) in astronomical systems by studyingrotation curves. We will start with a simple case: our solar system.Keplerian Orbits4) Let's consider the planets orbiting the Sun. They actually travel in ellipses, but theirorbits are nearly circular. As you did for the ants, write a formula for the speed of aplanet around the Sun in terms of its distance from the Sun, R. Use the period, P,the time required for one orbit. Rearrange your speed formula to solve for P.forZ TT BRecall the proportionality relation form of Kepler's Law of planetary motion, P² x a³.Note that a is the same as R when we're approximating the planetary orbits as circles, souse R for the distance.5) Use the expression you wrote down in question 4) relating speed (v), period (P), anddistance from the Sun (R), to eliminate P from the proportionality form of Kepler's Law(P2 x a³). You should be left with an expression only in terms of speed (v) and distance(R). Simplify your answer.6) Rearrange this proportionality to solve for speed (v) in terms of distance (R).Based on this expression, you now know how the speed of a planet varies with distancefrom the Sun. We will be taking a closer look at the actual rotation curve of the solar systemand its relation with the solar system's mass distribution.Continues on next page →3

Answered: Image /qna-images/answer/bcc07a04-15e5-4760-a670-abfdbbb07bc5.jpg

5) Use the expression you wrote down in question 4) relating speed (v), period (P), and distance from the Sun (R), to eliminate P from the proportionality form of Kepler's Law (P2 x a³). You should be left with an expression only in terms of speed (v) and distance (R). Simplify your answer.

5) Use the expression you wrote down in question 4) relating speed (v), period (P), and distance from the Sun (R), to eliminate P from the proportionality form of Kepler's Law (P2 x a³). You should be left with an expression only in terms of speed (v) and distance (R). Simplify your answer.

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter13: Gravitation

Section: Chapter Questions

Problem 45P: The Sun orbits the Milky Way galaxy once each 2.60108 years, with a roughly circular orbit averaging...

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HELLO HELP WITH NUMBER 5 PLEASE, COMPLETE SOLUTION, 4 DECIMAL PLACES. AND GRAPH THANK YOUU