Newton's Law of Universal Gravitation
Fg = GM1M2 / R2
Since Fg = m * a, we have
a = Fg / m = GMe / Re2
Where Me is earth's mass, and Re is radius of earth in meters.
G is gravitational constant, G = 6.67 x 10-11 N * m2 / kg2
a = 9.8 m/s2 = g
Note that the value of g is not constant but varies inversely with the earth radius squared Re2
Gravitational Energy
Potential energy of an object on earth with mass M0
PE = -GM0Me / Re (from Fg = GM1M2 / R2 and E = F * Δd)
Since a = Fg / m = GMe / Re2 = g
We have
PE = - M0 * a * Re = - M0 * g * Re
From above, when we lift an object with mass m from the ground by a height of h, the work done will be:
ΔPE = mgh
Escape Velocity
The escape velocity is the minimum initial velocity required for an object to leave a planet, for example, earth.
(1/2)M0Vesc2 = GM0Me / Re
Vesc2 = 2 G Me / Re
Note escape velocity depend on the mass of the earth but not on the mass of the object!
Note: this section is not required in SAT Physics
Orbit Velocity
The orbit velocity can be determined by assuming that we have an approximately circular orbit. In this case, the centripetal force equals the gravitational force:
GM0Me / Re2 = M0 Vorbit2 / Re
Vorbit2 = G Me / Re
Note orbit velocity depend on the mass of the earth but not on the mass of the object.
Note: this section is not required in SAT Physics