Gravitational Forces & Orbits of Planets

Gravitational Force

100

In Newton‘s law of universal gravitation, the magnitude of gravitational force is calculated as:

F_g = G((m₁m₂)/r²)

200

If the distance between two masses doubles, what happens to the magnitude of gravitational force between them 

It becomes 1/4th as large 

300

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 

400

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

500

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.

F_g = ((GMm)/R³)r

Gravitational Potential Energy

100

Formula for gravitational potential energy between two masses

U_G = -G((m₁m₂)/r)

200

As a satellite moves farther from Earth, what happens to its gravitational potential energy 

It increases (becomes less negative)

300

Sign of work done by gravity during inward motion (+/-)

positive 

400

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 

500

A satellite is moved from orbit radius R to 3R. What is its change in gravitational potential energy

ΔU = (2GMm)/(3R)

Satellite Motion

100

What provides the centripetal force on satellites

gravity

200

What is the equation for the centripetal force required to keep a satellite in orbit 

F_c = (mv²)/r

300

What is the orbital speed of a satellite orbiting mass M at radius r

v = sqrt((GM)/r)

400

If the orbital radius of a satellite doubles, what happens to its speed

It decreases by a factor of sqrt(2)

500

Derive the orbital period T of a satellite orbiting a planet of mass M at radius r

T = 2pi*sqrt(r³/(GM))

Kepler’s Laws

100

Kepler’s First Law

The orbit of a planet is an ellipse with the Sun at one of the two foci

200

Kepler’s Second Law

A planet moves faster when closer to the sun and slower when farther away (law of equal areas)

300

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)

400

Planet A has an orbital radius R and orbital period T_A. If Planet B of equal mass has orbital radius 4R, what is its orbital period in terms of T_A?

T_B = 8T_A

500

Does the angular momentum of a satellite change as its speed and distance change

no