A satellite travels in a circular orbit around Earth and has a period of 300 min

Question

A satellite travels in a circular orbit around Earth and has a period of 300 minutes. Determine the distance of the satellite from the surface of the Earth. If a simple pendulum has a period of 2.8 s on the earth, what will be its period on the moon? On the moon, the acceleration due to gravity is 1/6 of that on the earth. What is the length of the pendulum? A 2.8 kg block attached to a spring oscillates, without friction, with amplitude of 0.25 m. If the spring constant is 86 N/m find the maximum speed of the block. (V=1.39m/s)

Explanation / Answer

5. T = 2 pi / w

w = 2 pi / T

for circular motion,

G M m / r^2 = m w^2 r

G M = w^2 r^3

G M = (2 pi / T)^2 r^3

6.67 x 10^-11 x 5.972 x 10^24 = ( 2pi / (300 x 60))^2 r^3

r = 14.84 x 10^6 m

and r = Re + h

14.84 x 10^6 = 6.372 x 10^6 + hh

h = 8.47 x 10^6 m Or 8470 km

6. T = 2pi sqrt[L/g]

on earth T = 2.8s and g = m/s^2

2.8 = 2 pi sqrt(L/9.8)

L = 1.95 m .........Ans

on moon: T' = 2 pi sqrt[ 6L/g]

T' = 2.8 x sqrt(6) = 6.86 sec

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