Problem 7: A planet has 80 times the earth\'s mass and five times its radius. It
ID: 1616241 • Letter: P
Question
Problem 7: A planet has 80 times the earth's mass and five times its radius. It has a circular orbit with a period of24 years about a star with three times the sun's mass. (For the purposes of this problem assume the Earth has a circular orbit) (9 points each) Part (a): What is the planet's orbital radius in AU, where l AU is the earth-sun distance? Part (b): An astronaut has an earth weight of 125 lbs. What is her weight on the surface of this planet? Problem 8: In Chapter 5 we looked at the following example where a bucket filled with dirt was used to acceler-Explanation / Answer
let r1 is the radius of orbit of the Earth around the sun.
r1 = 1 AU
Time period of the Earth around the sun, T1 = 1 year
let r2 is the radius of orbit of Planet around the sun.
T2 = 24*T1
a) we know, T^2 is proportional to r^3
T2^2/T1^2 = (r2/r1)^3
(T2/T1)^(2/3) = r2/r1
==> r2 = r1*(T2/T1)^(2/3)
= 1*(24/1)^(2/3)
= 8.32 AU <<<<<<<<------------------Answer
2) acceleration due to gravity on the earth, g = G*Me/Re^2
acceleration due to gravity on the given planet,
g_planet = G*M_planet/R_planet^2
= G*80*Me/(5*Re)^2
= (80/25)*G*Me/Re^2
= 3.2*g
so, weight becomes 3.2 time
weight of the person on the given planet = 125*3.2
= 400 lb <<<<<<<<------------------Answer