A satellite gets unstable in its orbit and starts to fall towards earth and also starts heating. If the satellite had a potential energy of 1000 j initially and by the time it reaches earth's surface, it attains a kinetic energy of 500 j. Then, how much energy is spent in the form of heat?
Answers
Answer:
Circular orbits arise whenever the gravitational force on a satellite equals the centripetal force needed to move it with uniform circular motion.
Fc = Fg
mv2 = GMm
rp rp2
v2 = Gm1
r
Substitute this expression into the formula for kinetic energy.
K = ½m2v2
K = ½m2 ⎛
⎝ Gm1 ⎞
⎠
r
K = ½ Gm1m2
r
Note how similar this new formula is to the gravitational potential energy formula.
K = + ½ Gm1m2
r
Ug = − Gm1m2
r
K = −½Ug
The kinetic energy of a satellite in a circular orbit is half its gravitational energy and is positive instead of negative. When U and K are combined, their total is half the gravitational potential energy.
E = K + Ug
E = −½Ug + Ug
E = ½Ug
E = − Gm1m2
2r
The gravitational field of a planet or star is like a well. The kinetic energy of a satellite in orbit or a person on the surface sets the limit as to how high they can "climb" out of the well. A satellite in a circular orbit is halfway out (or halfway in, for you pessimists).