Question from Principles of Astrophysics: Using Gravity and Stellar Physics to E

Question

Question from Principles of Astrophysics: Using Gravity and Stellar Physics to Explore the Cosmos

Please Answer step-by-step!

3. Each part of this question covers a key concept. Each requires at most a few sentences to answer; some are much shorter. Please be concise. (a) Suppose that the Sun were instantaneously replaced by a star with twice as much mass. Would Earth's orbit stay the same? Explain your answer. Now suppose that Earth doubled in mass instantly but the Sun remained the same. Would Earth's orbit stay the same? Explain your answer (b) How do Kepler's laws contradict the idea that all planets are in uniform circular b) How do Kepler's laws contrad motion around the Sun? (c)Equation Jeopardy: Create a question for which the following equation gives the 2 * 6.67 × 10-8crn3g-s-2 * 1.99 × 1033g 6.96 × 1010cm

Explanation / Answer

a.

yes. Orbiting bodies orbit their mutual center of gravity (barycenter). In the Sun-Earth system, the barycenter is very close to the center of the Sun because of the Sun's immense mass. A more massive Earth would change that orbit a tiny bit but, since the Sun's mass is so great, the effect would be negligible.

b.

Uniform circular motion basically says that all orbits are perfect circles with the orbiting body on the circumference and the primary at the centre. However, Kepler identified that orbits are not perfect circles; they are ellipses with the primary at one focus. While the actual shape of the orbit is very close to circular, the mathematics behind each shape are very different. Because they say different things, they are contradictory.

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