a) Suppose you are at the earth\'s equator and observe a satellite passing direc

Question

a) Suppose you are at the earth's equator and observe a satellite passing directly overhead and moving from west to east in the sky. Exactly 16.0 hours later, you again observe this satellite to be directly overhead. Assume a circular orbit. How far above the earth's surface is the satellite's orbit?

h = ?m

b)You observe another satellite directly overhead and traveling east to west. This satellite is again overhead in 16.0 hours. How far is this satellite's orbit above the surface of the earth?

h = ?m

Problem 13.55 Part A uppose you are at the earth s equato and observe a satellite passing directly overhead and mowing fro st east in the sky. Exactly 16.0 hours later you again observe this satellite to be overhead A directly Submit My Answers Giv up You observe srolher salelile diectly overhead and trseveling east lowest This estelile is agein overhead in 16.0 hours How ta is tris setelit a orbit above the surface of My An a circular orbi How arabowe the earths surface is the satellite's orbit Co

Explanation / Answer

Earths mass (m) = 5.98 e-24 kg
G (a constant) = 6.673 e-11 N
Earths surface radius (R) = 6.371 e-6 meters
r = satellite orbital radius in meters

a.
Earths sidereal rotation rate = 7.2921 e-5 rad/sec

Earths rotation in 16 hours ( 46,800 sec ) = 57,600 * 7.2921 e-5 = 4.2002 radians

Rotation by satellite to catch up = ( 2 * pi ) + 4.2002 = 10.4802 radians

Sattelite rotation rate required = 10.4802 / 57,600 = 1.81 e-4 rad / sec

Equation :
rad/sec = v / r , and v = square root ( G * m / r ), so :

rad /sec = ( square root ( ( G * m ) / r ) ) / r

Transpose to feature r :

r = cube root ( ( G * m ) / ( rad / sec ² ) )

r = 1.81 e-7 meters (satellite orbital radius)

Satellite altitude = r - R = 1.39 e-7 meters

b)Earths sidereal (360°) rotation time = 23.93446 h = 86,164 seconds

Earths rotation in 16 hours = ( 2 * pi ) * ( 57,600 / 86,164 ) = 4.198 radians

Rotation of satellite = ( 2 * pi ) - 4.198 = 2.082 radians

Rotation rate of satellite = 2.802 / 57,600 =3.615 e-5 rad / sec

r = cube root ( ( G * m ) / ( rad / sec ² ) )
r = 4.7337 e-7 meters

Altitude = r - R = 4.314 e-7 meters

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