Law of Universal Gravitation Virtual Laboratory

Physics / Astrophysics / Classical Mechanics

Gravitational Apparatus

Mode: Vary Distance — Drag masses or use slider to change separation
r = 50.0 m F₁₂ F₂₁ M₁ = 500 kg M₂ = 500 kg 💡 Drag either mass horizontally to adjust distance r interactively

Live Measurements

LIVE
Mass 1 (M₁) 500 kg
Mass 2 (M₂) 500 kg
Distance (r) 50.0 m
Gravitational Force (F) 6.674 × 10⁻⁹ N F = F₁₂ = F₂₁ (Equal & Opposite)

Experimental Parameters

kg
1 kg 500 kg 1000 kg
kg
1 kg 500 kg 1000 kg
m
1 m 50 m 100 m

Force vs Distance Analytical Graph

Inverse-Square Law Plot (F ∝ 1/r²)
Theoretical F = G·m₁·m₂ / r² Current Experimental State (r, F)

1. About Universal Gravitation

Formulated by Sir Isaac Newton in 1687, the Law of Universal Gravitation states that every particle of matter in the universe attracts every other particle 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.

2. Working Principle & Equation

F = G · (m₁ · m₂) / r²
  • F: Gravitational attraction force between masses (in Newtons, N).
  • m₁, m₂: Magnitudes of the two interacting masses (in kilograms, kg).
  • r: Separation distance measured center-to-center (in meters, m).
  • G: Universal Gravitational Constant ≈ 6.67430 × 10⁻¹¹ N·m²/kg².

3. Guided Experiment Procedure

  1. Set Mass 1 (M₁) to an initial value (e.g., 500 kg).
  2. Set Mass 2 (M₂) to an initial value (e.g., 500 kg).
  3. Select Mode 1 (Vary Distance) and adjust distance r from 10 m to 90 m.
  4. Observe the real-time force magnitude and vector arrows as distance r changes.
  5. Observe the non-linear hyperbolic decay curve on the Force vs Distance graph.
  6. Switch to Mode 2 (Vary Mass 1) or Mode 3 (Vary Mass 2) to observe linear force dependency.
  7. Click Verify Experiment to evaluate force symmetry (F₁₂ = F₂₁) and law compliance.

4. Astrophysics & Engineering Applications

Universal gravitation governs phenomena across macro and astronomical scales:

  • Planetary & Lunar Orbits: Keeps Earth in orbit around the Sun and the Moon around Earth.
  • Artificial Satellites: Used by aerospace engineers to calculate orbital velocity and altitude for GPS, weather, and telecommunication satellites.
  • Ocean Tides: Explains gravitational tidal pulling caused by the Moon and Sun on Earth's oceans.
  • Galactic Structure: Holds stars together in galaxies and binds galaxy clusters across cosmic distances.