A planet has 80 times the earth\'s mass and five times its radius. It has a circ

Question

A planet has 80 times the earth's mass and five times its radius. It has a circular orbit with a period of 24 years about a star with three times the sun's mass. (For the purposes of this problem assume the Earth has a circular orbit) What is the planet's orbital radius in AU, where 1 AU is the earth-sun distance? An astronaut has an earth weight of 125 lbs. What is her weight on the surface of this planet? In Chapter 5 we looked at the following example where a bucket filled with dirt was used to accelerate a cart up the incline using a massless rope and pulley. We found that the acceleration had the following form a = m_Bg - m_C g sin (15)/m_B + m_C where m_B and m_C are the mass of the bucket and cart respectively. Imagine now a more real case where the rope is still massless but pulley is not. As an additional constraint, there is enough friction between the rope and the pulley that the rope does not slip. Will the acceleration increase or decrease compared to our previous result and explain how you came to that

Explanation / Answer

7(b) g' = GMp/Rp2 = G.80Me/(25Re2)

g' = gp = (16/5)g

So, weight on earth, mg = 125 lbs

Weight on planet, mg' = mg(16/5) = 125*16/5 = 400 lbs

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