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# Relative Initial Speed Calculated

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Vanguard 1, launched in 1958, is the oldest human artefact/satellite in orbit. It weighs 1.47 kg and orbits the Earth every 134.2 minutes. At its closest distance it is 654 km from the surface of the Earth. Assume that it is in a circular orbit and due to a collision with some space junk it loses 20% of its velocity.

a) Calculate its initial speed
b) Calculate the initial energy of the satellite-Earth system
c) Calculate the energy of the satellite-Earth system after the collision
d) Explain why the satellite loses altitude and spirals into the Earth after the collision

##### Solution Summary

Relative initial speed calculations are examined. The initial energy of the satellite-earth systems are calculated.

##### Solution Preview

Vanguard 1, launched in 1958, is the oldest human artefact / satellite in orbit. It weighs 1.47 kg and orbits the Earth every 134.2 minutes. At its closest distance it is 654 km from the surface of the Earth. Assume that it is in a circular orbit and due to a collision with some space junk it loses 20% of its velocity.
a) calculate its initial speed
b) calculate the initial energy of the satellite-Earth system
c) calculate the energy of the satellite-Earth system after the collision
d) explain why the satellite loses altitude and spirals into the Earth after the collision

Solution: Speed, angular frequency, time period etc. of the satellite are functions of its height above earth's surface. In an elliptical orbit, these parameters keep varying as satellite's distance from earth changes. However, in this problem it is to be assumed that the satellite's orbit is circular; further, the time period is also specified. However, the specified ...

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