Viscous force increase the velocity of satellite. Explain.

1.	Viscous force increase the velocity of satellite. Explain.
Answer» When a satellite of mass m revolves in a circular orbit of radius r, around the earth of mass m, the gravitational attraction of earth provides the required centripetal force i.e., \(\frac{mv^2}{r}\) = \(\frac{GMm}{r^2}\) or mv²r = GMm or (mvr)v = a constant or Lv = a constant ..............(i) where mvr = L, angular momentum of a satellite. According to a law of conservation of momentum if no external torque acts on the satellite, then its angular momentum L is conserved. Since, the air friction will provide a retarding torque to satellite, therefore, there will be decrease in angular momentum of the satellite in air. As a result of it, the velocity of satellite increase according to relation (i).

Answer»

When a satellite of mass m revolves in a circular orbit of radius r, around the earth of mass m, the gravitational attraction of earth provides the required centripetal force

i.e., \(\frac{mv^2}{r}\) = \(\frac{GMm}{r^2}\)

or mv²r = GMm

or (mvr)v = a constant

or Lv = a constant ..............(i)

where mvr = L, angular momentum of a satellite.

According to a law of conservation of momentum if no external torque acts on the satellite, then its angular momentum L is conserved. Since, the air friction will provide a retarding torque to satellite, therefore, there will be decrease in angular momentum of the satellite in air. As a result of it, the velocity of satellite increase according to relation (i).

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