two satellites, one lighter and the other twice as massive, describe different o
ID: 1865290 • Letter: T
Question
two satellites, one lighter and the other twice as massive, describe different orbits around the earth, the lighter one going on an orbit of radius twice the radius of the heavier one, 2m, r, 2r. 1.) consider one single satellite, say the lighter one. write down the equation for the gravitational force exerted by the Earth on this satellite. 2.) write down Newton second law for this satellite to go in a circular orbit. 3.) determine the equation for the velocity of the satellite so that it goes in a circle. 4.) what is the ration of the speed of the lighter satellite to the velocity of the heavier satellite.
Explanation / Answer
a)
m = mass of lighter satellite
M = mass of earth
2r = radius of orbit
force by earth on lighter satellite is given as
F = GMm/(2r)2
2)
for the circular orbit , gravitational force by earth = centripetal force
GMm/(2r)2 = m v2/(2r)
3)
v = sqrt(GM/(2r))
4)
Ratio = sqrt(rheavy/rlight) = sqrt(2r/r) = 1.41
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.