A 1-ton (2000 lb) spacecraft is in a circular orbit around the Earth. Its veloci

Question

A 1-ton (2000 lb) spacecraft is in a circular orbit around the Earth. Its velocity relative to the center of the Earth is 17,000 MPh (miles per hour). What is its velocity, v. in m/s (meters/sec)? What is the kinetic energy. Ek. of the spacecraft relative to the center of the Earth in units of: The centripetal force. F = Mv2/r. is equal to the gravitational force. Fg = kgMM/r2. acting on the orbiting spacecraft, where: M = mass of the spacecraft (I ton) M = mass of the Earth (5.9Sxl0 24 kg) kg = universal gravitational constant (6.67x10 -11 m2/kg-s2) r = separation distance between center of mass of the Earth and center of mass of the spacecraft If the mean diameter of the Earth, de. is 12.742 km. find the height, h, of the spacecraft above the surface of the Earth in units of:

Explanation / Answer

c )

Using the condition ::

Ms V2 /r = kg Ms Me /r2

V2 = kg Mg / r

r = kg Mg / V2

inserting the values

r = (6.67 x 10-11) (5.98 x 1024) / (7.6 x103)2

r = 6.906 x 106 m

radius of earthm ,R = diameter/2 = 12742 x 103 /2 = 6.371 x 106 m

we know that , r = R + h

6.906 x 106 m = 6.371 x 106 m + h

h = 5.35 x 105 m

h = 332 miles

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