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## Homework Statement

A satellite of the Earth has a mass of 1550 kg. It orbits Earth with a mean radius of orbit of 7.00 x 10^6 m.

a) What is the gravitational potential energy of the satellite with respect to Earth?

b) What is the kinetic energy and the velocity of the satellite in Earth’s orbit?

c) What is the binding energy of the satellite to Earth?

d) What is the total mechanical energy of the satellite in its orbit?

## Homework Equations

PEg = -Gm1m2/R

Vescape = root(2)(G)(m1)/Rm

E binding = 1/2<PEg> in orbit[/B]

## The Attempt at a Solution

**a)PEg = -(6.67 X 10^-11)(5.98 X 10^24)(1550)/(1.338 X 10^7)**

= -4.62 X 10^10J

b) Vescape = root(2)(6.67 x 10^-11)(5.98 x 10^24)/(6.38 x 10^6)

= 1.12 x 10^4 m/s

KE = (1/2)(m)(V)^2

KE = (1/2)(1550)(1.12 x 10^4)^2

KE = 9.72 x 10^10J

c) E binding = 1/2<PEg> in orbit

(0.5)(4.62 X 10^10J) = 2.31 x 10^10J

= -4.62 X 10^10J

b) Vescape = root(2)(6.67 x 10^-11)(5.98 x 10^24)/(6.38 x 10^6)

= 1.12 x 10^4 m/s

KE = (1/2)(m)(V)^2

KE = (1/2)(1550)(1.12 x 10^4)^2

KE = 9.72 x 10^10J

c) E binding = 1/2<PEg> in orbit

(0.5)(4.62 X 10^10J) = 2.31 x 10^10J

d) I'm not certain which equation I should use for this one