A space probe is fired as a projectile from the Earth\'s surface with an initial

Question

A space probe is fired as a projectile from the Earth's surface with an initial speed of 1.62 Times 10^4 m/s. What will its speed be when it is very far from the Earth? Ignore atmospheric friction and the rotation of Earth. A 965-kg satellite orbits the Earth at a constant altitude of 101-km. How much energy must be added to the system to move the satellite into a circular orbit with altitude 204 km/What is the change in the system's kinetic energy? What is the change in the system's potential energy?

Explanation / Answer

Vi = initial speed at the surface = 1.62 x 104 m/s

Vf = final velocity

R = radius of earth = 6.4 x 106 m

M = mass of earth

m = mass of space probe

using conservation of energy

(0.5) m Vi2 - GMm/R = (0.5) m Vf2

(0.5) (1.62 x 104 )2 - (6.67 x 10-11) (5.98 x 1024)/(6.4 x 106) = (0.5) Vf2

Vf = 11738.6 m/s = 1.17 x 104 m/s

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