Newton's law of universal gravitation states that any two objects attract each other with a force F = GM₁M₂/r², where G ≈ 6.67×10⁻¹¹ N·m²/kg², M₁ and M₂ are the masses, and r is the distance between their centers. It's an inverse-square law tested in AP Physics 1 Topic 2.6.
Newton's law of universal gravitation says every object with mass pulls on every other object with mass. The force is F = GM₁M₂/r². It gets bigger when either mass gets bigger, and it gets weaker fast as the objects move apart because of the r² in the denominator. The word "universal" is the whole point. The same rule that makes an apple fall also keeps the Moon orbiting Earth and Earth orbiting the Sun.
Two details matter for AP problems. First, r is measured center to center, not surface to surface, so for a satellite you add Earth's radius to its altitude. Second, the force is mutual. Earth pulls on you and you pull back on Earth with the exact same magnitude, which is Newton's third law hiding inside the gravity equation. The constant G ≈ 6.67×10⁻¹¹ N·m²/kg² is tiny, which is why you don't feel a pull from your desk. You only notice gravity when at least one mass is planet-sized.
This law is the core of Topic 2.6 (Gravitational Force) in Unit 2: Force and Translational Dynamics. It's where AP Physics 1 explains what weight actually is. The familiar F = mg isn't a separate law, it's universal gravitation evaluated at Earth's surface, where g = GM_Earth/r². That connection lets you calculate g on other planets, at high altitudes, or for any spherical mass, which is a classic exam move. It also sets up everything orbital. When gravity is the only force on a satellite, it acts as the centripetal force, so universal gravitation plugs directly into circular motion analysis. Proportional reasoning with this equation (what happens to F if r doubles or both masses double) is one of the most reliably tested skills in the unit.
Keep studying AP® Physics 1 Unit 2
Gravitational Field g = GM/r² (Unit 2)
Divide the gravitational force by the small mass and you get the field, g = GM/r². This is why g ≈ 9.8 m/s² near Earth's surface and why g shrinks as you climb. F = mg is just universal gravitation in disguise.
Newton's Third Law (Unit 2)
Gravitational forces always come in equal-and-opposite pairs. Earth pulls on the Moon exactly as hard as the Moon pulls on Earth. The Moon accelerates more only because its mass is smaller, not because the force is.
Circular Motion and Orbits (Unit 2)
For a satellite, gravity IS the centripetal force. Setting GM₁M₂/r² equal to mv²/r lets you solve for orbital speed or period, one of the most common setups combining these two topics.
Gravitational Potential Energy (Unit 3)
The force law has an energy partner, U = -GM₁M₂/r. Near Earth's surface this simplifies to the mgh you use in energy conservation, so universal gravitation quietly underwrites half of Unit 3.
Multiple-choice questions love proportional reasoning here. If you double the distance, the force drops to one fourth. If you double both masses, the force quadruples (2 × 2 = 4). You should be able to do these ratios without a calculator. Other common stems ask what G equals (about 6.67×10⁻¹¹ N·m²/kg²), how gravitational force depends on distance, or what gravitational mass means (the mass that determines how strongly gravity acts on an object). On free-response questions, universal gravitation usually shows up combined with something else, like setting gravity equal to mv²/r for an orbit, deriving g on another planet, or drawing a free-body diagram where gravity is the only force on a satellite. Watch the classic trap of forgetting that r is center-to-center distance.
F = mg is not a different law of gravity. It's the universal law F = GM₁M₂/r² with Earth's mass and radius already plugged in, so g = GM_Earth/R_Earth² ≈ 9.8 m/s². Use mg when an object stays near Earth's surface where g is basically constant. Use the full GM₁M₂/r² form when distance changes meaningfully, like satellites, moons, or comparing planets.
The gravitational force between two objects is F = GM₁M₂/r², where G ≈ 6.67×10⁻¹¹ N·m²/kg² and r is the center-to-center distance.
It's an inverse-square law, so doubling the distance cuts the force to one fourth, and tripling it cuts the force to one ninth.
Force is directly proportional to each mass, so doubling both masses makes the force four times bigger.
Weight (F = mg) is just universal gravitation evaluated at Earth's surface, which means g = GM/r² and you can compute g for any planet.
Gravitational forces are always attractive and always come in equal-and-opposite Newton's third law pairs.
In orbit problems, gravity supplies the centripetal force, so set GM₁M₂/r² equal to mv²/r.
It states that every pair of masses attracts each other with a force F = GM₁M₂/r², proportional to both masses and inversely proportional to the square of the center-to-center distance. G is about 6.67×10⁻¹¹ N·m²/kg².
No. At the International Space Station's altitude, gravity is still about 90% of its surface value. Astronauts feel weightless because they're in free fall around Earth, with gravity acting as the centripetal force, not because gravity vanished.
They're the same physics. F = mg is the universal law with Earth's mass and radius baked in, valid only near the surface where g ≈ 9.8 m/s². For satellites, other planets, or changing distances, use the full GM₁M₂/r² version.
The force quadruples, because force is proportional to the product of the masses (2 × 2 = 4). This exact proportional-reasoning question is a favorite on AP Physics 1 multiple choice.
No, they're different. G is the universal gravitational constant, about 6.67×10⁻¹¹ N·m²/kg², and it's the same everywhere in the universe. Lowercase g is the gravitational field strength, about 9.8 m/s² at Earth's surface, and it changes with location.
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