Gravitational Constant

The gravitational constant G (≈ 6.67 × 10⁻¹¹ N·m²/kg²) is the universal proportionality constant in Newton's law of universal gravitation, F = Gm₁m₂/r², setting how strong the attractive force is between any two masses anywhere in the universe.

Verified for the 2027 AP Physics C: Mechanics examLast updated June 2026

What is the Gravitational Constant?

The gravitational constant, written as G, is the number that converts "two masses separated by a distance" into an actual force in newtons. It lives inside Newton's law of universal gravitation, F = Gm₁m₂/r², and its value is about 6.67 × 10⁻¹¹ N·m²/kg². That tiny exponent is the whole story. Gravity is by far the weakest fundamental force, which is why you don't feel a pull toward your desk but you definitely feel one toward Earth (a mass of about 6 × 10²⁴ kg makes up for G's smallness).

The key word is universal. G is the same for an apple and the Earth, for two stars, for a satellite and a planet. It doesn't depend on what the objects are made of, where they are, or how fast they're moving. In AP Physics C, G is the bridge between Newton's force laws and everything gravitational, including deriving the familiar g ≈ 9.8 m/s² near Earth's surface and analyzing orbits with Newton's second law.

Why the Gravitational Constant matters in AP Physics C: Mechanics

G shows up wherever you apply Newton's laws to gravitational interactions, starting with the force-law foundations in Topic 2.3 (Newton's Laws of Motion) and carrying through to gravitation and orbital mechanics later in the course. Newton's third law is baked right into the formula. The Earth pulls on you with Gm₁m₂/r², and you pull back on the Earth with the exact same magnitude, because the equation is symmetric in the two masses. On the exam, G matters most as a derivation tool. You set Gm₁m₂/r² equal to mg to find g at a planet's surface, or equal to mv²/r to solve for orbital speed and period. If you can manipulate G fluently, an entire family of FRQ setups (find g on planet X, find the orbital radius of a satellite, derive escape speed) becomes plug-and-derive instead of panic.

How the Gravitational Constant connects across the course

Universal Law of Gravitation (Unit 2)

G is meaningless without this law. F = Gm₁m₂/r² is where G lives, and every gravitational problem on the exam starts by writing this expression down. The inverse-square dependence on r is what makes orbits and surface gravity behave the way they do.

Weight (Unit 2)

Weight near Earth's surface, mg, is just the universal gravitation formula in disguise. Set mg = GM_Earth·m/r² and the small mass cancels, giving g = GM/r². That one derivation, getting little g from big G, is one of the most reused moves in the course.

Mass (Unit 2)

G multiplies the product of two masses, which is why gravitational force scales with mass while gravitational acceleration doesn't. Drop the m in F = ma against F = GMm/r² and you see why all objects fall at the same rate regardless of their mass.

Newton's Third Law (Topic 2.3)

Because m₁ and m₂ enter the formula symmetrically, gravity is automatically a third-law pair. The Earth tugs on the Moon exactly as hard as the Moon tugs on the Earth. The accelerations differ wildly because the masses do, not because the forces do.

Is the Gravitational Constant on the AP Physics C: Mechanics exam?

G is given on the AP Physics C equation sheet inside the law of universal gravitation, so you never memorize its value for its own sake. What you do need is to know when to deploy it. Multiple-choice questions love proportional reasoning with G's formula, like asking how the force changes if r doubles (it drops to one quarter) or how g compares on a planet with twice Earth's mass and twice its radius. On FRQs, gravitational problems are usually derivations. You'll set GMm/r² equal to mg to find surface gravity, or equal to mv²/r (Newton's second law for circular motion) to derive orbital speed, period, or radius in terms of G, M, and r. No released FRQ asks you to define G itself, but almost every orbital-mechanics FRQ requires writing G correctly in the first line of a derivation. The most common point-loser is mixing up G and g mid-problem, so label them carefully.

The Gravitational Constant vs g (acceleration due to gravity)

Big G and little g are completely different quantities. G is a universal constant (6.67 × 10⁻¹¹ N·m²/kg²) that is the same everywhere in the universe and never changes. Little g is a local acceleration (about 9.8 m/s² at Earth's surface) that depends on which planet you're on and how far you are from its center. They're linked by g = GM/r², which means g is something you calculate from G, not a constant in its own right. On a different planet or at a different altitude, g changes; G never does.

Key things to remember about the Gravitational Constant

  • G is the universal proportionality constant in F = Gm₁m₂/r², with a value of about 6.67 × 10⁻¹¹ N·m²/kg², and it is the same everywhere in the universe.

  • G's tiny value explains why gravity feels weak between everyday objects but dominates at planetary scales, where masses are enormous.

  • Setting GMm/r² equal to mg and canceling m gives g = GM/r², which lets you calculate surface gravity on any planet from its mass and radius.

  • Setting GMm/r² equal to mv²/r is the standard move for deriving orbital speed, period, and radius on FRQs.

  • Because the formula is symmetric in m₁ and m₂, gravitational forces are automatically Newton's third law pairs of equal magnitude.

  • G is a universal constant while g is a local acceleration; G never changes, but g depends on the planet and your distance from its center.

Frequently asked questions about the Gravitational Constant

What is the gravitational constant in AP Physics C?

It's G, the universal constant in Newton's law of gravitation F = Gm₁m₂/r², equal to about 6.67 × 10⁻¹¹ N·m²/kg². It sets the strength of the gravitational attraction between any two masses.

Is the gravitational constant the same as 9.8 m/s²?

No. 9.8 m/s² is little g, the local acceleration due to gravity at Earth's surface, and it changes from planet to planet. Big G (6.67 × 10⁻¹¹ N·m²/kg²) is a universal constant that's the same everywhere; you actually calculate g from it using g = GM/r².

Do I need to memorize the value of G for the AP exam?

No. G appears on the AP Physics C equation sheet inside the law of universal gravitation. What you need is the skill of using it in derivations, like setting GMm/r² equal to mg or mv²/r.

Why is the gravitational constant so small?

Gravity is the weakest of the fundamental forces, and G's value (about 6.67 × 10⁻¹¹ in SI units) reflects that. Two 1 kg masses a meter apart attract with a force of less than 10⁻¹⁰ N. You only notice gravity when at least one mass is planet-sized.

Does the gravitational constant change on other planets?

No, G is identical everywhere in the universe. What changes on other planets is little g, the surface gravitational acceleration, because g = GM/r² depends on the planet's mass M and radius r.