Question

If a satellite is in a sufficiently low orbit, it will encounter air drag from the earth's atmosphere. Since air drag does negative work (the force of air drag is directed opposite the motion), the mechanical energy will decrease. If Edecreases (becomes more negative), the radius r of the orbit will decrease. If air drag is relatively small, the satellite can be considered to be in a circular orbit of continually decreasing radius.

Part A

A satellite with mass 2590 kg is initially in a circular orbit a distance 320 km above the earth's surface. Due to air drag, the satellite's altitude decreases to 205 km . Calculate the initial orbital speed.

Part B Calculate the increase in orbital speed. Part C Calculate the increase in orbital speed. Part D Calculate the change in kinetic energy. Part E Calculate the change in gravitational potential energy. Part F Calculate the change in mechanical energy.

Answer 1

NOTE - Part B and Part C are same !!!

a)

Calculate the initial orbital speed.

v = sqrt ( GM / r + h)

where M is mass of earth and r is radius of earth

v = sqrt ( 6.67e-11 * 5.97e24 / (6371 + 320) * 1000

v = 7714.44 m/s

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b)

Calculate the increase in orbital speed.

v = ( r/2) v = sqrt ( GM / (r + h)³)

v = 66.3 m/s

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c)

Calculate the change in kinetic energy.

K.E = GMmr / 2( r + h) ²

K.E = 6.67e-11 * 5.97e28 * 2590 * 115000 / 2 * 6691000²

K.E = 1.324e9 J

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d)

Calculate the change in gravitational potential energy

U = - 2 * K.E

U = - 2.65e9 J

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