Gravitational Force
In Newton‘s law of universal gravitation, the magnitude of gravitational force is calculated as:
Fg = G((m1m2)/r2)
Formula for gravitational potential energy between two masses
UG = -G((m1m2)/r)
What provides the centripetal force on satellites
gravity
Kepler’s First Law
The orbit of a planet is an ellipse with the Sun at one of the two foci
If the distance between two masses doubles, what happens to the magnitude of gravitational force between them
It becomes 1/4th as large
As a satellite moves farther from Earth, what happens to its gravitational potential energy
It increases (becomes less negative)
What is the equation for the centripetal force required to keep a satellite in orbit
Fc = (mv2)/r
Kepler’s Second Law
A planet moves faster when closer to the sun and slower when farther away (law of equal areas)
Two objects exert gravitational forces on each other. One has much greater mass. Which object experiences the larger force?
Neither; they experience equal and opposite forces
Sign of work done by gravity during inward motion (+/-)
positive
What is the orbital speed of a satellite orbiting mass M at radius r
v = sqrt((GM)/r)
Kepler’s Third Kaw
The square of a planet’s orbital period is directly proportional to the cube of the semi-major axis (average distance)
Planet X has three times Earth’s mass and twice Earth’s radius. What is the gravitational acceleration at its surface in terms of Earth’s g
(3/4)g
If a satellite is moved from orbit of radius r to a higher orbit of 2r, is the change in gravitational potential energy greater than, less than, or equal to the change in kinetic energy
greater than
If the orbital radius of a satellite doubles, what happens to its speed
It decreases by a factor of sqrt(2)
Planet A has an orbital radius R and orbital period TA. If Planet B of equal mass has orbital radius 4R, what is its orbital period in terms of TA?
TB = 8TA
A tunnel is drilled through a uniform density planet of radius R and mass M. Find the gravitational force on a mass m located at a distance r from the center of the planet.
Fg = ((GMm)/R3)r
A satellite is moved from orbit radius R to 3R. What is its change in gravitational potential energy
ΔU = (2GMm)/(3R)
Derive the orbital period T of a satellite orbiting a planet of mass M at radius r
T = 2pi*sqrt(r3/(GM))
Does the angular momentum of a satellite change as its speed and distance change
no