Gravity Formula

The Formula

F = \frac{Gm_1 m_2}{r^2} (universal gravitation)

When to use: Everything pulls on everything else—but only huge things (like Earth) pull noticeably.

Quick Example

Earth pulls you down; you also pull Earth up (but it doesn't move noticeably).

Notation

G is the universal gravitational constant (6.674 \times 10^{-11} N m^2 kg^{-2}), m_1 and m_2 are the two masses in kilograms, and r is the centre-to-centre distance in metres.

What This Formula Means

The universal attractive force between any two objects with mass, decreasing with the square of distance.

Everything pulls on everything else—but only huge things (like Earth) pull noticeably.

Formal View

Newton's law of universal gravitation states that every point mass attracts every other point mass with a force F = \frac{Gm_1 m_2}{r^2}, directed along the line joining their centres.

Worked Examples

Example 1

easy
Calculate the gravitational force between Earth (M = 5.97 \times 10^{24} \text{ kg}) and a 1 \text{ kg} object at Earth's surface (r = 6.37 \times 10^6 \text{ m}). Use G = 6.674 \times 10^{-11} \text{ N m}^2/\text{kg}^2.

Solution

  1. 1
    Apply Newton's law of gravitation: F = \frac{GMm}{r^2}
  2. 2
    Substitute: F = \frac{6.674 \times 10^{-11} \times 5.97 \times 10^{24} \times 1}{(6.37 \times 10^6)^2}
  3. 3
    Calculate: F = \frac{3.98 \times 10^{14}}{4.06 \times 10^{13}} \approx 9.8 \text{ N}

Answer

F \approx 9.8 \text{ N}
This calculation confirms that g \approx 9.8 \text{ m/s}^2 at Earth's surface. Gravity is the attractive force between any two masses, governed by the universal law of gravitation.

Example 2

easy
A ball is dropped from rest near Earth's surface. How fast is it going after 3 \text{ seconds}? Ignore air resistance and use g = 9.8 \text{ m/s}^2.

Example 3

medium
Calculate the gravitational force between two 50 \text{ kg} masses separated by 2 \text{ m}. Use G = 6.674 \times 10^{-11} \text{ N m}^2/\text{kg}^2.

Common Mistakes

  • Using the distance between surfaces instead of the distance between the centres of mass of the two objects.
  • Forgetting to square the distance r in the denominator, which drastically changes the result.
  • Confusing g (gravitational field strength, ~9.8 m/s²) with G (the universal gravitational constant, 6.67 × 10⁻¹¹ N m²/kg²).

Why This Formula Matters

Governs planetary motion, ocean tides, and keeps us on Earth's surface.

Frequently Asked Questions

What is the Gravity formula?

The universal attractive force between any two objects with mass, decreasing with the square of distance.

How do you use the Gravity formula?

Everything pulls on everything else—but only huge things (like Earth) pull noticeably.

What do the symbols mean in the Gravity formula?

G is the universal gravitational constant (6.674 \times 10^{-11} N m^2 kg^{-2}), m_1 and m_2 are the two masses in kilograms, and r is the centre-to-centre distance in metres.

Why is the Gravity formula important in Physics?

Governs planetary motion, ocean tides, and keeps us on Earth's surface.

What do students get wrong about Gravity?

Gravity never 'turns off' in space—astronauts float because they're falling around Earth.

What should I learn before the Gravity formula?

Before studying the Gravity formula, you should understand: force, mass.

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Related Concepts

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