Question

15. The kinetic energy of the satellite
orbiting around the Earth is
(a) equal to potential energy
(b) less than potential energy
(c) greater than kinetic energy
(d) zero​

Answer 1

Answer:

first you follow me

Explanation:

and thank me

Answer 2

Answer:

The following four statements about circular orbits are equivalent. Derive any one of them from first principles.

Negative kinetic energy equals half the potential energy (−K = ½U).

Potential energy equals twice the total energy (U = 2E).

Total energy equals negative kinetic energy (E = −K).

Twice the kinetic energy plus the potential energy equals zero (2K + U = 0).

This is a key relationship for a larger problem in orbital mechanics known as the virial theorem.

solution

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 = GMmrprp2v2 = Gm1r

Substitute this expression into the formula for kinetic energy.

K = ½m2v2

K = ½m2⎛

⎜

⎝Gm1⎞

⎟

⎠rK = ½ Gm1m2r

Note how similar this new formula is to the gravitational potential energy formula.

K = + ½ Gm1m2rUg = − Gm1m2r

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 = − Gm1m22r

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).

Magnify

practice problem 2

Determine the minimum energy required to place a large (five metric ton) telecommunications satellite in a geostationary orbit.

solution

Start by determining the radius of a geosynchronous orbit. There are several ways to do this (which includes looking it up somewhere), but the traditional way is to start from the principle that the centripetal force on a satellite in a circular orbit is provided by the gravitational force of the Earth on the satellite. Combine this with the formula for the speed of an object in uniform circular motion. The algebra is somewhat tedious and has been condensed in the derivation below.