A 1000 kg satellite orbits the Earth at a constant altitude of 100 km. How much energy must be added to the system to move the satellite into a circular orbit with altitude 200 km? Discuus the changes in kinetic energy, potential energy, and total energy.
Formulae thay may help:
E = - GMm/2r
Energy change = Energy final - Energy initial
where G = 6.67 * 10^-11 N*m^2/kg^2
M(Earth) = 5.98 * 10^24 kg
m = mass of satellite
Please help especially those University Students taking PHYS113 or in higher level.
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Answers (1)
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Answerer 1
It can be proved that the total energy, TE1 of the satellite orbiting at a distance of r1, TE2 at a distance of r2 from the centre of earth is given by
TE1 = - 0.5 GMm/r1 and TE2 = -0.5 GMm/r2.
Change in energy, E = TE2 - TE1= 0.5GMm[1/r1 - 1/r2] or
because r1 = R + 100x10^3 and r2 = R + 200x10^3 where R is the radius of earth.
E = [0.5 GMm/(R+100x10^3)(R+200x10^3)](r2 - r1)
= [0.5 GMm/(R+100x10^3)(R+200x10^3)](100x10^3)
= 0.5 (GMm/R^2(100x10^3)/[(1+(100x10^3/R)(1+20…
= 0.5x1000x9.8x100x10^3/[(1+ 100/6400)(1+ 200/6400)]
= 4.9x10^8/[(1+1/64)(1+2/64)]
= 4.9x10^8/[(1.015625)(1.03125)] = 4.68 x 10^8 JSign in to vote!
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