Gravitation is the attractive force between any two objects with mass, with magnitude F = GMm/r², proportional to the product of the masses and inversely proportional to the square of the distance between their centers. In AP Physics C Mechanics, it drives orbital motion, escape velocity, and Kepler's laws.
Gravitation is the universal attraction between masses. Newton's law of universal gravitation says the force between two objects has magnitude F = GMm/r², where G is the gravitational constant, M and m are the masses, and r is the distance between their centers. The force always pulls the objects toward each other along the line connecting them, and it never turns off; it just gets weaker as r grows (cut the distance in half, the force quadruples).
Here's the mental shift AP Physics C asks you to make. The familiar weight force mg is just universal gravitation evaluated near Earth's surface, where r barely changes so the force looks constant. Once an object moves far from a planet (satellites, rockets, moons), you have to use the full 1/r² law, which means a position-dependent force, a gravitational potential energy of U = -GMm/r instead of mgh, and circular or elliptical orbits instead of parabolic projectile paths.
Gravitation threads through almost the entire Mechanics course. It enters as a force in your free-body diagrams and Newton's second law work, then reappears in the energy unit as the classic example of a conservative force with a potential energy function. It comes back one more time when you analyze orbiting satellites, where gravity supplies the centripetal force and Kepler's laws fall out of F = GMm/r² plus circular motion. It's also one of the best showcases of calculus in the course. Because the force depends on position, finding gravitational potential energy means integrating F over distance, which is exactly the kind of derivation Physics C loves. If you can set up and solve a gravitation problem from scratch, you've proven you can handle forces, energy, circular motion, and calculus all at once.
Keep studying AP Physics C: Mechanics Unit XFAHq6btBZc5gQPX
Universal Law of Gravitation (Unit 2)
This is the equation form of gravitation, F = GMm/r². It slots into Newton's second law just like any other force, so a satellite problem is really just a free-body diagram where gravity is the only force acting.
Kepler's Laws (Unit 6)
Kepler's laws are gravitation's consequences for orbits. Setting GMm/r² equal to mv²/r for a circular orbit gives you Kepler's third law (T² ∝ r³) in a few lines, which is one of the most-asked derivations in orbital mechanics.
Escape Velocity (Unit 3)
Escape velocity is gravitation meets energy conservation. Set kinetic energy plus U = -GMm/r equal to zero (just barely reaching infinity with no speed left) and solve for v. The negative sign on U is doing the real work here.
Work-Energy Theorem (Unit 3)
Gravitation is the course's go-to example of a conservative force. Because the work it does is path-independent, you can define U = -GMm/r and skip the force analysis entirely in many problems, which is usually the faster route on the exam.
Gravitation shows up two ways. Near a planet's surface, it's the constant mg in basically every dynamics and energy problem; released FRQs like 2019 Q1 (object falling through fluid) and 2024 Q2 (cylinder falling with drag F = bv) start from gravity as the driving force and ask you to build differential equations around it. Far from a surface, it becomes its own problem type: derive orbital speed or period from F = GMm/r² and circular motion, derive Kepler's third law, compute total orbital energy, or find escape velocity using U = -GMm/r. Expect symbolic answers in terms of G, M, m, and r, and expect at least one step that requires calculus, like integrating the force to get potential energy. The most common point-losers are using mgh instead of -GMm/r when altitude changes are large, and dropping the negative sign on gravitational potential energy.
They're the same force in two costumes. Weight mg is the universal gravitation formula with r locked at the planet's radius, so the force looks constant and U = mgh works fine. Once the distance from the planet's center changes meaningfully (rockets, satellites, moons), mg breaks down and you must use F = GMm/r² with U = -GMm/r. Quick test: if r changes during the problem, you need the full law.
Newton's law of universal gravitation, F = GMm/r², gives the attractive force between any two masses, and it weakens with the square of the distance between their centers.
Weight mg is just universal gravitation evaluated at a planet's surface, so use mg only when the object stays close to the surface.
Gravitational potential energy far from a surface is U = -GMm/r, and it is negative because you'd have to add energy to pull the masses apart to infinity.
For a circular orbit, gravity is the centripetal force; setting GMm/r² = mv²/r lets you derive orbital speed, period, and Kepler's third law.
Escape velocity comes from energy conservation: an object escapes when its kinetic energy equals the magnitude of its gravitational potential energy, giving v = √(2GM/r).
Gravitation is a conservative force, so the work it does is path-independent and you can solve most problems with energy conservation instead of force analysis.
Gravitation is the attractive force between any two masses, given by F = GMm/r². On the exam it powers everything from falling-object FRQs (where it appears as mg) to orbital mechanics problems involving satellites, escape velocity, and Kepler's laws.
Both, depending on scale. Use U = mgh when the object stays near a planet's surface and g is effectively constant. Use U = -GMm/r whenever the distance from the planet's center changes significantly, like a rocket launch or a satellite orbit. Using mgh on an orbit problem is one of the most common ways to lose FRQ points.
Because the zero point is set at infinite separation. Gravity is attractive, so any two masses at a finite distance have less energy than if they were infinitely far apart, which makes U = -GMm/r negative. A bound orbit always has negative total energy, and that fact is exactly what the escape velocity derivation exploits.
No. At the International Space Station's altitude, gravity is still about 90% of its surface strength. Astronauts float because they and the station are both in continuous free fall around Earth, with gravity acting as the centripetal force. 'Weightless' means free fall, not zero gravity.
Gravitation is the force law (F = GMm/r²); Kepler's laws describe the orbital motion that force produces. The classic AP derivation combines gravitation with circular motion to prove Kepler's third law, T² = (4π²/GM)r³, showing the laws aren't separate facts but consequences of the inverse-square force.
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