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Viktor [21]
3 years ago
8

A satellite of mass m circles a planet of mass M and radius R in an orbit at a height 2R above the surface of the planet. What m

inimum energy is required to change the orbit to one for which the height of the satellite is 3R above the surface of the planet
Physics
1 answer:
Goryan [66]3 years ago
6 0

Answer:

ΔE = GMm/24R

Explanation:

centripetal acceleration a = V^2 / R = 2T/mr

T= kinetic energy

m= mass of satellite, r= radius of earth

= gravitational acceleration = GM / r^2

Now, solving for the kinetic energy:

T = GMm / 2r = -1/2 U,

where U is the potential energy

So the total energy is:

E = T+U = -GMm / 2r

Now we want to find the energy difference as r goes from one orbital radius to another:

ΔE = GMm/2 (1/R_1 - 1/R_2)

So in this case, R_1 is 3R (planet's radius + orbital altitude) and R_2 is 4R

ΔE = GMm/2R (1/3 - 1/4)

ΔE = GMm/24R

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