In: Physics
NASA has asked your team of rocket scientists about the feasibility
of a new satellite launcher...
NASA has asked your team of rocket scientists about the feasibility
of a new satellite launcher that will save rocket fuel. NASA's idea
is basically an electric slingshot that consists of 4 electrodes
arranged in a horizontal square with sides of length d at a height
h above the ground. The satellite is then placed on the ground
aligned with the center of the square. A power supply will provide
each of the four electrodes with a charge of +Q/4 and the satellite
with a charge -Q. When the satellite is released from rest, it
moves up and passes through the center of the square. At the
instant it reaches the square's center, the power supply is turned
off and the electrodes are grounded, giving them a zero electric
charge. To test this idea, you decide to use energy considerations
to calculate how big Q will have to be to get a 100 kg satellite to
a sufficient orbit height. Assume that the satellite starts from 15
meters below the square of electrodes and that the sides of the
square are each 5 meters. In your physics text you find the mass of
the Earth to be 6.0 x 1024 kg and its average radius is 6370
km