what are (a) the speed and (b) the period of a 220 kgsatellite in an approximate

Question

what are (a) the speed and (b) the period of a 220 kgsatellite in an approximately circular orbit 640 km above thesurface of earth suppose it losses the mechanical energy at theaverage rate of 1.4 x 105 J per orbital revolutionadopting the reasonable approximation that the satellites orbitbecomes a circle oof slowly dimnishing radius determines thesatellites (c) altitude (d) speed (e) period at the end of its 1500th revolution (f) what is the magnitude of average retarding forceon the satellite, is the angular momentum around earths centerconserved for (g) the satellite (h) the satellite earth system

Explanation / Answer

(a)

    the speed will be
    v = [(6.67 x 10-11m3 / s2 . kg) (5.98 x 1024 kg) /(7.01 x 106 m)]
= ........ m / s
(b)
    T = 2 r / v
   = ....... s
(c)
   if Eo is the initial energy then theenergy after n orbits is
   E = Eo - n C
   C = 1.0 x 105 J / orbit
   for a circular orbit the energy and the orbitradius are related by
   E = - G M m / 2 r
   so the radius of the n orbit is given by
   r = - G M n / 2 E
   Eo = ........ J
   the energy after 1500 orbits is given by
   E = Eo - n C
      = .......... J
   orbit radius will be
   r = ........ m
   h = r - R
      = ........ m
(d)
   the speed will be
   v = (G M / r)
      = ......... m / s
(e)
   the period will be   
   T = 2 r / v
      = ......... min
(f)
   magnitude of the average retarding force on thesatellite will be
   F = - E / s
      = .......... N
(g)
   the resistive force exerts a torque on thesatellite so its angular momentum is not conserved
(h)
   the satellite earth system is essentiallyisolated so its momentum is verynearly conserved

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