Newton's Law of Gravitation

Newton’s law of gravitation says that every mass pulls on every other mass, and the pull gets stronger when either mass is larger. It also weakens quickly with distance because the separation is squared, so doubling the distance makes the force four times smaller. The constant G sets the overall scale of gravity in SI units and was measured experimentally; the inverse-square form matches the way a central force spreads out in three-dimensional space.

Use this formula when you need the gravitational force between two objects that can be treated as point masses or as spherically symmetric bodies. It is common in astronomy and orbital mechanics, such as finding the attraction between planets and moons, satellites and Earth, or estimating weight-like forces at a distance.

• Forgetting to square the distance r in the denominator
• Using kilometres or metres inconsistently instead of converting everything to SI units
• Mixing up mass and weight, or using the wrong value for G