A satellite that weighs 4900 N on the launchpad travels around the earth\'s equa

Question

A satellite that weighs 4900 N on the launchpad travels around the earth's equator in a circular obit with a period of 1.667 h. The earth's mass is 5.97 x 1024kg, its equatorial radius is 6.3 x 106 m, and G = 6.67 x 10-11 N*m2/kg2.

(a) Calculate the magnitude of the earth's gravitational force on the satellite. [Correct ANS: 3910N]

(b) Determine the altitude of the satellite above the Earth's SURFACE. [Correct ANS: 7.55x105 m]

I would really appreciate if you could show me how to get those answers! Thank you so very much. :)

Explanation / Answer

(A) at equator,

W = m g

m = 4900 /9.8 = 500 kg

w = 2 pi / T = 2 pi / (1.667 x 3600 s) = 1.047 x 10^-3 rad/s

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

r^3 = G M / w^2 = (6.67 x 10^-11) (5.97 x 10^24) / (1.047 x 10^-3)^2

r = 7.135 x 10^6 m

Fg = G M m / r^2 = 3910 N  

(b) r = R + h

7.135 x 10^6 = 6.371 x 10^6 + h

h = 7.6 x 10^5 m

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