Escape Velocity

How fast does a space probe have to go to escape from the Earth?


Their Way
 
A space probe slows down as it moves away from the Earth. A space probe escapes from the Earth if its velocity hits zero when the probe gets to an infinite distance from the Earth.


If the velocity of a probe is zero, the kinetic energy of the probe is zero.


The gravitational potential energy of a probe at an infinite distance is zero.


If kinetic energy and gravitational potential energy are both zero, mechanical energy is zero.


The mechanical energy of a probe remains the same once the probe is launched. So the mechanical energy of the probe when it was launched was zero.


The formula for mechanical energy is:


ME = KE + GPE


The formula for escape velocity is:


KE + GPE = 0


KE = −GPE


½ mv ² = GMm  ⁄  r


v ² = 2GM  ⁄  r



My Way
 
As velocity goes up, weight goes down. If a space probe is moving fast enough, its weight is zero. The probe is then no longer held to the Earth and it escapes.

The formula for weight is:


W = RW − KE


The formula for escape velocity is:


0 = RW − KE

KE = RW

½ mv ² = GMm  ⁄  r

v ² = 2GM  ⁄  r