1 SATELLITES AND GRAVITATION John Parkinson © 2 SATELLITES.
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SATELLITES AND GRAVITATIONJohn Parkinson
Newtons Law of GravitationM1M2r
SATELLITESmvEquation of MotionM
SATELLITE VELOCITYvmFor an orbit CLOSE to the surfaceF = mgv = 8 km/s
SATELLITE PERIODmEquation of MotionM
GE0SYNCHRONOUS COMMUNICATIONS SATELLITETO REMAIN OVER ONE PLACE ON THE EARTHS SURFACE, THE PERIOD HAS TO BE THE SAME AS THE EARTHS DAY.
COMMUNICATIONS SATELLITETHIS GIVES A RADIUS OF 42 000 km
VGDefinition The gravitational potential at a point is the work done in moving unit mass (1kg) from infinity to that point.But potential energy at infinity is zero no attraction.Hence the gravitational potential at the point really measures the absolute potential energy that 1 kilogram has at that point. FOR A RADIAL FIELDUNITSJ kg-1
The gravitational potential at a point measures the potential energy per kilogram at that point. JoulesThe potential energy of a mass of m kilograms is given by:Ep = mVG
gRelationship between Field Strength and PotentialAt any point Field Strength = POTENTIAL GRADIENT
How much energy is needed to move a 200 tonne spaceship from A to B?POTENTIAL DIFFERENCE, VG = - 10 ( - 40 ) = 30 MJ kg-1EP = m VG = 200 000 kg x 30 MJ kg-1ENERGY NEEDED = 6 TJ
TOTAL ENERGY OF A SATELLITEmvM
ORBITAL DECAYmvMWhen a satellite enters the atmosphere, drag heats it up. It falls to a lower orbit and SPEEDS UP.The decrease in total energy is only half of the decrease in potential energy.As r decreases, the potential energy becomes numerically larger but decreases overall as it is more negative. The kinetic energy is numerically equal to the total energy, but is positive, so increases.