Gravitation: every key term you need (+ practice quiz)

More AP Physics C guides

• Kinematics
• Newton's Laws of Motion
• Work, Energy and Power
• Systems of Particles and Linear Momentum
• Rotational Motion

Newton's Law of Universal Gravitation

F = Gm₁m₂/r²; every pair of masses attracts along the line joining them; an inverse-square central force.

Gravitational Constant

G = 6.67 × 10⁻¹¹ N·m²/kg²; the universal constant setting the strength of gravity; small, so gravity is weak on lab scales.

Gravitational Field

g = F/m = GM/r²; the gravitational force per unit mass at a point; a vector pointing toward the source mass.

Surface Gravity

g = GM/R²; the field at a planet's surface; gives 9.8 m/s² for Earth using its mass and radius.

Inverse-Square Dependence

Gravitational force and field fall off as 1/r²; doubling the distance cuts the force to one quarter.

Gravitational Potential Energy

U = −GMm/r; the energy of a two-mass system taking U = 0 at infinite separation; always negative for a bound pair.

Why U is Negative

Work must be done against attraction to separate masses to infinity, so bound configurations have U < 0.

Relation Between F and U

F = −dU/dr; differentiating U = −GMm/r gives F = −GMm/r², the attractive gravitational force.

Circular Orbit Condition

Gravity supplies the centripetal force: GMm/r² = mv²/r, giving orbital speed v = √(GM/r).

Orbital Speed

v = √(GM/r); the speed for a circular orbit of radius r; smaller orbits require higher speeds.

Orbital Period

T = 2π√(r³/GM); the time for one circular orbit; follows from v = 2πr/T and v = √(GM/r).

Kepler's First Law

Planets move in ellipses with the Sun at one focus; circular orbits are the special case of zero eccentricity.

Kepler's Second Law

A line from the Sun to a planet sweeps equal areas in equal times; a consequence of angular momentum conservation.

Kepler's Third Law

T² ∝ r³ (or a³); the square of the period is proportional to the cube of the orbital radius (semi-major axis).

Total Energy of an Orbit

E = KE + U = −GMm/(2r) for a circular orbit; the total mechanical energy is negative for a bound orbit.

Kinetic Energy in Orbit

KE = ½mv² = GMm/(2r); exactly half the magnitude of the potential energy (virial relation).

Escape Velocity

v_esc = √(2GM/R); the minimum launch speed for total energy zero, allowing escape to infinity from the surface.

Escape vs Orbital Speed

v_esc = √2 × v_orbit; escape speed is √2 times the circular orbital speed at the same radius.

Gravity Inside a Shell

A uniform spherical shell exerts no net gravitational force on a mass inside it; the field there is zero.

Gravity Inside a Uniform Sphere

Only mass within radius r contributes, so g ∝ r inside a uniform planet, rising linearly from zero at the center.

Weightlessness in Orbit

Orbiting astronauts are in continuous free fall; both they and the station accelerate together, giving zero apparent weight.