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Physics: Universal Gravitation Calculator

Calculate gravitational force using F = G(m₁m₂)/r². Includes preset masses for Earth, Moon, Sun, and other celestial bodies with scientific notation output.

F = G(m₁m₂) / r²

G = 6.674 × 10⁻¹¹ N·m²/kg²

Gravitational Force

1.9804 × 1020
Newtons (N)
Mass 15.9720 × 1024 kg
Mass 27.3420 × 1022 kg
Distance3.8440 × 108 m
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What is The Mechanics of Gravitational Attraction?

Published in 1687, Sir Isaac Newton's Law of Universal Gravitation established that every single particle of mass in the entire universe physically attracts every other particle. The force scales directly with their combined mass, but drops off exponentially with distance.

Mathematical Foundation

Newton's Law of Universal Gravitation
F=Gm1m2r2F = G \frac{m_{1}m_{2}}{r^2}
FF= Gravitational force between the two centers of mass (Newtons, N)
GG= Gravitational Constant (6.674 × 10⁻¹¹ N·m²/kg²)
m1m_{1}= Mass of the first object (kg)
m2m_{2}= Mass of the second object (kg)
rr= Absolute distance between the precise centers of the two objects (m)

Laws & Principles

  • The Inverse Square Law: The r² denominator means distance is exponentially powerful. Doubling the distance between two objects does not cut the gravity in half—it cuts it down to 25% (one quarter).
  • The Microgravity Illusion: Astronauts on the International Space Station (400km up) are not floating because they lack gravity. Earth's gravity there is still nearly 90% as strong as on the surface. They float because they are moving sideways so fast that they constantly 'miss' the Earth as they fall (free-fall orbit).
  • The Impossibly Weak Constant: The 'G' constant (6.674 × 10⁻¹¹) is incredibly small. This is why you don't feel the gravitational pull of your car or house. Gravity is actually the weakest of the four fundamental forces of physics.

Step-by-Step Example Walkthrough

" Calculate the gravitational force between a 70 kg human and the Earth (5.972 × 10²⁴ kg) if the human is standing exactly on the surface (radius = 6,371,000 meters). "

  1. 1. Identify the masses: m1 (Human) = 70 kg, m2 (Earth) = 5.972 × 10²⁴ kg.
  2. 2. Identify the radius to center: r = 6,371,000 meters.
  3. 3. Multiply masses by G: 6.674×10⁻¹¹ * 70 * 5.972×10²⁴ = 2.788 × 10¹⁶.
  4. 4. Divide by r²: 2.788×10¹⁶ / (6371000)²
Final Result: The final resulting force is approximately 686 Newtons. This is mathematically identical to calculating the human's normal 'weight' down on Earth using W = mg (70 kg * 9.8 m/s²).

Quick Answer: How do I calculate gravitational pull?

This calculator finds the force of gravity using the standard Formula F = G(m₁m₂)/r². Enter the two masses (in kilograms) and the distance between their cores (in meters). The calculator processes the 10⁻¹¹ constant and automatically outputs the absolute pulling force in standard Newtons.

Mathematical Formula

F = G(m₁m₂) / r²

Where G is the Universal Gravitational Constant (6.67408 × 10⁻¹¹ m³ kg⁻¹ s⁻²), resolving into Newtons of force.

Orbital Body Reference (Reference Table)

Standard celestial body weights to use in custom macroscopic calculations.

Celestial Object Mass (kg) Radius to Core (meters)
The Sun1.989 × 10³⁰695,700,000
Jupiter1.898 × 10²⁷69,911,000
Earth5.972 × 10²⁴6,371,000
Mars6.390 × 10²³3,389,500
Earth's Moon7.342 × 10²²1,737,400

Astrophysics Case Scenarios

Satellites in LEO (Low Earth Orbit)

To keep a 1,000 kg communication satellite from falling back to Earth, engineers cannot change the gravitational force. They must calculate the exact orbital velocity required so the centrifugal force perfectly balances the F = G(Mm)/r² equation, keeping the satellite artificially suspended.

Lunar Tidal Pull

The Moon is extremely light compared to Earth, but it is incredibly close (384,000 km). Because distance is squared in the denominator, the proximity overpowers the Sun's massive weight advantage, allowing the Moon's gravity to literally drag billions of tons of ocean water across the planet daily.

Physics Best Practices

Do This

  • ✓Measure from the core. When calculating gravity for someone standing on a planet, the distance (r) is not zero. "r" must be the full radius length from the exact molten core of the planet straight up to the person's center-mass.

Avoid This

  • ✗Don't mix up g and G. Lowercase "g" is the acceleration of gravity specifically on Earth (9.81 m/s²). Capital "G" is the Universal standard constant (6.674 × 10⁻¹¹) applied to the entire cosmos. They are completely different variable types.

Frequently Asked Questions

Is gravity different on top of Mount Everest?

Yes. Because you are 8,848 meters higher up, the 'r' denominator in the equation gets slightly larger. The resulting downward force drops. You would weigh roughly 0.28% less on Everest than at sea level.

Does the Moon pull Earth, or does Earth pull the Moon?

Both pull with the exact same Newtons of force. Newton's 3rd Law dictates equal and opposite reactions. The difference is that the Earth is so incredibly massive that this force barely moves it, while the lighter Moon experiences massive acceleration from the identical force.

Who calculated the G Constant?

Isaac Newton invented the math framework, but Henry Cavendish physically measured G in 1798 using a perfectly balanced torsion balance inside a sealed wooden box to measure the micro-gravity between lead spheres.

Is gravity a force or curved spacetime?

Einstein's General Relativity proved that gravity is actually the geometric curving of 4D spacetime, not a classical physical "pull". However, for almost all non-black-hole engineering scenarios, Newton's classical equation provides functionally perfect calculations.

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