Gravitational Force Calculator

General Physics

Calculate the gravitational force between two objects based on Newton's Law of Universal Gravitation.

Practical Examples

Explore these real-world scenarios to understand how the gravitational force calculation is applied.

Force between Earth and Moon

Earth and Moon

Calculate the gravitational force exerted between the Earth and the Moon.

m1: 5.972e24 kg, m2: 7.347e22 kg

r: 3.844e8 m

Force between Sun and Earth

Sun and Earth

Calculate the gravitational force that keeps the Earth in orbit around the Sun.

m1: 1.989e30 kg, m2: 5.972e24 kg

r: 1.496e11 m

Force between two Bowling Balls

Two Bowling Balls

Calculate the tiny gravitational force between two standard 7kg bowling balls placed 1 meter apart.

m1: 7 kg, m2: 7 kg

r: 1 m

Force on the ISS

International Space Station

Calculate the gravitational force on the International Space Station (ISS) from Earth. ISS mass is ~419,725 kg and orbits at ~408 km altitude from surface.

m1: 5.972e24 kg, m2: 419725 kg

r: 6778000 m

Other Titles
Understanding the Gravitational Force Calculator
A Comprehensive Guide to Newton's Law of Universal Gravitation and Its Applications

What is Gravitational Force?

  • The Universal Attraction
  • Newton's Groundbreaking Law
  • The Gravitational Constant (G)
Gravitational force is a fundamental interaction in the universe that causes mutual attraction between all things that have mass. The more mass an object has, the stronger its gravitational pull. This force is what keeps planets in orbit around the sun, holds galaxies together, and keeps our feet firmly on the ground.
The Formula: F = G (m1m2)/r^2
Sir Isaac Newton formulated the law of universal gravitation, which states that every particle attracts every other particle in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The constant of proportionality, G, is known as the gravitational constant, a very small number (approx. 6.67430 × 10^-11 N·m²/kg²), indicating that gravity is the weakest of the four fundamental forces of nature.

Step-by-Step Guide to Using the Gravitational Force Calculator

  • Selecting Your Calculation Target
  • Inputting Your Data Correctly
  • Interpreting the Results
Our calculator is designed for ease of use and flexibility. Here's how to get your results:
1. Choose what to calculate
Start by selecting which variable you want to solve for from the dropdown menu: Force (F), Mass 1 (m1), Mass 2 (m2), or Distance (r).
2. Enter the known values
Fill in the input fields for the known variables. Make sure to select the correct units (kilograms/grams for mass, meters/kilometers for distance). For very large or small numbers, you can use scientific notation (e.g., 5.972e24 for the mass of the Earth).
3. Calculate and Analyze
Click the 'Calculate' button. The result will be displayed in the 'Calculation Result' section in SI units (Newtons for force, kilograms for mass, meters for distance).

Real-World Applications of Gravitational Force

  • Celestial Mechanics and Astronomy
  • Space Exploration and Satellite Orbits
  • Geophysics and Tides
The calculation of gravitational force is crucial in many scientific and engineering fields.
Astronomy
Astronomers use it to predict the movements of planets, stars, and galaxies. It's essential for understanding phenomena like planetary orbits, the formation of celestial bodies, and the dynamics of binary star systems.
Spacecraft Trajectories
Engineers designing missions to other planets or deploying satellites must precisely calculate gravitational forces from the Sun, Earth, and other celestial bodies to ensure correct trajectories and stable orbits.
Geophysics
The gravitational pull of the Moon and Sun on Earth's oceans is the primary cause of tides. Geologists also study minute variations in Earth's gravitational field to understand subsurface structures and locate mineral deposits.

Common Misconceptions and Correct Methods

  • Mass vs. Weight
  • Distance Between Centers, Not Surfaces
  • Gravity in Space
There are several common misunderstandings about gravity.
Mass is not Weight
Mass is the amount of matter in an object and is constant everywhere. Weight is the force of gravity acting on that mass (Weight = mass × g). An astronaut has the same mass on Earth and the Moon, but their weight is much less on the Moon due to its lower gravity.
The Importance of 'r'
The distance 'r' in Newton's formula is the distance between the centers of the two objects, not the distance between their surfaces. This is a critical distinction, especially when objects are close or very large, like planets.
Zero Gravity is a Myth
Astronauts in orbit are not in 'zero gravity'. They are in a continuous state of free-fall around the Earth. At the altitude of the ISS, Earth's gravity is still about 90% as strong as on the surface. The feeling of weightlessness comes from falling at the same rate as their spacecraft.

Mathematical Derivation and Examples

  • Deriving the Formula for Other Variables
  • Worked Example: Earth and Sun
  • Units and Conversions
Newton's formula can be rearranged to solve for any of its variables.
Solving for Mass or Distance

Starting with F = G (m1m2)/r^2, we can isolate other variables:

  • To find distance (r): r = sqrt(G m1 m2 / F)
  • To find a mass (e.g., m1): m1 = F r^2 / (G m2)
Example Calculation

Let's calculate the force between the Earth (m1 ≈ 5.97e24 kg) and a 70 kg person (m2) on its surface. The Earth's radius (r) is about 6.37e6 m. F = (6.674e-11 5.97e24 70) / (6.37e6)^2 F ≈ (2.789e16) / (4.058e13) F ≈ 687 Newtons. This is the person's weight.