NASA has a mission to put a satellite into an equatorialgeosynchronous orbit, so

Question

NASA has a mission to put a satellite into an equatorialgeosynchronous orbit, so that its orbital motion will keep it abovelongitude 150 as the Earth rotates beneath it. This is done inthree steps:
1) The satellite is placed into a circular equatorial orbit 220miles above the surface

2) The satellite's propulsion system is used to increase itsvelocity in order to place it into an elliptical transfer orbitwith perigee 220mi and apogee at the distance of the circulargeosynchronous orbit.

3) The velocity of the satellite at apogee is changed in order toinsert it into the circular geosynchronous orbit

Assuming that the exhaust velocity of the satellite rocket is2500m/sec and the final mass in geosynch. orbit is 676kg, calculatethe mass of fuel expended by the satellite's rocket in order toraise it from its 220 mile circular orbit

Explanation / Answer

the thrust acting on the rocket is F = (dm/dt) * v the thrust acting on the rocket is equal to the centripetalforce acting on the rocket when it is moving in a circularorbit F = (m * v^2/r) or (dm/dt) * v = (m * v^2/r) or (dm/dt) = (m * v/r) m = 676 kg,v = 2500 m/s and r = 220 mile = 220 * 1609.344 m =354055.68 m Here,(dm/dt) gives the mass of fuel expended by thesatellite's rocket in order to raise it from its 220 mile circularorbit.

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