A satellite with mass 1 ton (=1000kg) is placed into a geosynchronous orbit, i.e

Question

A satellite with mass 1 ton (=1000kg) is placed into a geosynchronous orbit, i.e. one with period that matches that of Earth. Assume that G = 6.6 * 10^-11 N m^2/kg^2 and Earth's mass M = 2*10^24 kg A) What must the radius of such orbit be? How fast is this satellite moving once in orbit? B) How much energy is required to reach it from Earth's surface (Earth's radius R = 6371km)? C) How much does the satellite weigh once in orbit? D) How much of Earth's surface is visible from the geosynchronous orbit, roughly?

Explanation / Answer

1.

(A) T = 24 hrs = 24 x 3600 sec

w = 2pi / T = 7.27 x 10^-5 rad/s

FOr circular motion,

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

G M = w^2 r^3

(6.6 x 10^-11) ( 2 x 10^24) = (7.27 x10^-5)^2 r^3

r = 2.922 x 10^7 m ......Ans

v = w r = 2124.6 m/s

(B) PEi = - G M m / Re = - 20718882.44m

KEi = ?

PEf = - G M m / r = - 4517144.6 m

KEfg = - PE/2 = 2258572.31m

energy cosnervation,

PEi + KEi = Pef + KEf

KEi = 1.87 x 10^8 J

(C) W = G M m / r^2 = 156.24 N

(D) surace area = 2 pi Re^2 = 2.55 x 10^14 m^2

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