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A 550 kg satellite is in a circular orbit at an altitude of 450 km above the Ear

ID: 1510901 • Letter: A

Question


A 550 kg satellite is in a circular orbit at an altitude of 450 km above the Earth's surface. Because of air friction, the satellite eventually falls to the Earth's surface, where it hits the ground with a speed of 1.70 km/s. How much energy was transformed into internal energy by means of air friction? A satellite of mass 2.6 kg is in an elliptical orbit around the Earth(mass 5.98e + 24 kg). The satellite's mimimum distance from the center of the Earth is 9200000 m, at which point it has a speed of 8300 m/s. For this orbit find the total energy of the satellite-Earth system.

Explanation / Answer

1) let PE be the gravitation potential energy of a satellite at a distance of 450 km from the surface of the earth

                   at a height , h the total energy of the satellite is in the form of potential energy

                      PE = m g h

         = 550 kg * 9.8 m/sec^2 * 450 * 10^3 m

                           = 2.426 * 10 ^ 9 Joules

by the time the satellite hit the ground the some of the energy was transformed into internal energy by means of air friction, and the rest of the potentential energy converted into kinetic energy KE

Frictinal energy = PE- KE

                          KE = m * v ^2 / 2 = 550 kg * (1.7 * 10^3 ) ^2 / 2

                                                        KE = 7.95 x 10^ 8 Joules

                Frictinal energy = PE-KE = 24.26 * 10 ^ 8 Joules – 7.95 x 10^ 8 Joules

                                                              = 16.31 * 10^ 8 Joules is the energy which was transformed into internal energy by means of air friction.

2) For this orbit, the total energy of the satellite–Earth system which is given as :

Etotal = K.Esat + P.Eearth

Etotal = (1/2) ms v2 + mE g h

Etotal = (0.5) (2.6 kg) (8300 m/s)2 + (5.98 x 1024 kg) (9.8 m/s2) [(9200000 m) + (6371000 m)]

Etotal = (89557000 J) + (912522884 x 1024 J)

Etotal = 1.002 x 1033 J

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