Flashcards in 10.3 Motion In A Gravitational Field Deck (8)
What is the derivation for the gravitational force when a point mass m orbits a spherical mass M the orbital radius is r and the orbital speed is v?
The gravitational force provides the centripetal force on m and so
GMm/r^2 = m(v^2/r) -------> v^2 = GM/r
The formula says that the loser m is to M the faster it moves.
What is the speed for circular motion in general?
v = 2pir/T where T is the period (the time for one full revolution).
What is Kepler's third law?
It relates the period to the orbital redius. Taking M to be the mass of the sun and m the mass of a planet we deduce by coming the last two formulas that
(2pir/T)^2 = GM/r -------> T^2 = (4pi^2/GM)r^3
How is the total energy of a moving satellite defined?
A satellite orbits a spherical mass M. The kinetic energy of the orbiting satellites is
Ek - 1/2mv^2 and since v^2 = GM/r we have that Ek = 1/2(GMm/r) The total energy is therefore
Et = Ep + Ek = 1/2(GMm/r) - GMm/r = -1/2(GMm/r)
the total energy is negative.
What is significant about the satellite being a potential well?
Energy must be supplied if it is to move away.
What is escape speed?
The minimum launch sped of a projectile at the surface of a planet so that the projectile can move far away (to infinity).
What is the total energy at launch at the surface of the planet?
Et = Ek + Ep = 1/2mv^2 - GMm/R where R is the radius of the earth.