Motion of Orbiting Satellites - AP Physics C: Mechanics

$E = -\frac{GMm}{2r}$. Sum of kinetic and gravitational potential energies.

Gravitational force. Earth's gravity provides the centripetal force for circular orbits.

$F = \frac{GMm}{r^2}$. Newton's law of gravitation with Earth's mass $M$ and distance $r$.

$T^2 \text{ is proportional to } r^3$. Square of period proportional to cube of semi-major axis.

A line joining a planet and the Sun sweeps out equal areas in equal time intervals. Conservation of angular momentum causes variable orbital speeds.

Planets move in elliptical orbits with the Sun at one focus. Describes elliptical shape with Sun at focal point.

$v = \frac{2 \pi r}{T}$. Circumference divided by period for uniform circular motion.

$U = -\frac{G M m}{r}$. Negative value indicates bound system with zero reference at infinity.

$F = \frac{mv^2}{r}$. Force directed toward center required for circular motion.

$F = G \frac{m_1 m_2}{r^2}$. Newton's law of universal gravitation between two point masses.

$6.674 \times 10^{-11} \text{ N m}^2/\text{kg}^2$. Universal gravitational constant in SI units.

The period remains unchanged. Period depends only on orbital radius, not satellite mass.

Orbital period is 24 hours. Matches Earth's rotational period for stationary positioning.

$V = -\frac{G M}{r}$. Gravitational potential energy per unit mass.

Gravitational force. Earth's gravity provides the centripetal force for circular orbits.

Orbital speed decreases. Higher orbits have slower speeds per $v = \sqrt{GM/r}$.

$F = G \frac{m_1 m_2}{r^2}$. Newton's law of universal gravitation between two point masses.

$K = \frac{1}{2} \frac{GMm}{r}$. Half the gravitational potential energy magnitude.

$\text{Angular velocity} = \frac{2 \pi}{T}$. Rate of angular displacement for orbital revolution.

$g = \frac{GM}{r^2}$. Gravitational acceleration at any distance from planet center.

The period decreases. Larger planetary mass creates stronger gravitational field.

$a_c = \frac{v^2}{r}$. Acceleration toward center for circular orbital motion.

Orbital speed decreases. Inverse relationship from $v = \sqrt{GM/r}$ formula.

$F = \frac{GMm}{(R + h)^2}$. Gravitational force decreases with square of distance.

It is equal to the orbital radius. Semi-major axis equals radius for circular orbital geometry.

It will spiral inward. Energy loss causes orbital decay toward the planet.

$V = -\frac{G M}{r}$. Gravitational potential energy per unit mass.

$\text{Specific energy} = -\frac{GM}{2r}$. Total energy per unit mass for orbital motion.

Orbital period is 24 hours. Matches Earth's rotational period for stationary positioning.