Universal Gravitation

Sir Isaac Newton formulated the law of universal gravitation in 1687, proposing that every particle of matter attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. Use the interactive model to examine reciprocal force vectors, calculate exact force magnitudes across variable distances, and test the inverse-square falloff.

Interactive experiment: verify inverse-square scaling

Open the Universal Gravitation module. The module provides sliders for Mass 1 (m1), Mass 2 (m2), Distance (r), and Gravitational Constant (G Scale), alongside toggles for force vectors and gravitational field lines.

1. Set Mass 1 (m1) to 100 kg, Mass 2 (m2) to 100 kg, Distance (r) to 10 m, and Gravitational Constant (G Scale) to 1. Check the readout card to confirm Force (F) reads exactly 100.00 N and both vector arrows F₁₂ and F₂₁ point towards the opposite mass with equal magnitude.
2. Drag Distance (r) from 10 m to 20 m. Confirm that the force readout decreases from 100.00 N to 25.00 N, demonstrating the factor of 4 reduction predicted by the inverse-square law.
3. At Distance (r) = 20 m, increase Mass 1 (m1) from 100 kg to 200 kg. Observe that Force (F) doubles from 25.00 N to 50.00 N, confirming linear scaling with mass.
4. Adjust Distance (r) to the boundary minimum of 2 m while keeping m₁ = 100 kg, m₂ = 100 kg, and G Scale = 1. Observe that Force (F) reaches 2500.00 N without graphical clipping or numerical overflow.

The on-screen vector arrows resize dynamically to indicate force magnitude while clamping their display length so that arrows never overlap when the masses are positioned close together.