Force falls with distance squared
Double the distance and the attraction becomes one quarter as strong. Hover the curve to move the test object.
Drag the test object or launch it sideways. Change mass and distance to see the orbit, vectors, and equations respond.
Gravity is not a hidden rope. It is the measurable way mass-energy shapes motion, usefully predicted by Newton and more deeply explained by Einstein.
Double the distance and the attraction becomes one quarter as strong. Hover the curve to move the test object.
F = G m₁m₂ / r²
Mass increases attraction linearly; distance weakens it quadratically.
The floor pushes upward on you, producing the sensation called weight.
Why does an orbiting satellite keep missing Earth?
This page contains a static illustration and a JavaScript calculator, not a numerical orbital integrator. Begin with central mass one and distance eight, displayed as eight thousand kilometres. The implemented acceleration is nine point eight one times mass times the square of six point three seven one divided by distance. Change distance to sixteen, or sixteen thousand kilometres. Doubling the denominator quarters the acceleration. Compare the two exact held bars at sixty five pixels per metre per second squared. The result follows the calculator formula; it does not demonstrate an actual moving trajectory. Return the distance to eight, then change central mass from one to two. The source formula is linear in this mass input, so acceleration doubles. The force readout multiplies that acceleration by the fixed source factor zero point four zero six. It therefore doubles too. The top bars use thirty four pixels per metre per second squared; the lower bars use seventy pixels per newton. Their different scales are labelled, so do not compare force-bar length directly with acceleration-bar length. These are two exact input states held side by side, and the fixed force factor does not change with central mass. The lower graph uses a normalized inverse-square value, seven divided by distance, squared. Its curve is not labelled in acceleration units. Start at distance seven: the normalized quantity is one. Changing distance to fourteen makes it one quarter. Changing again to twenty eight makes it one sixteenth. The three coloured markers use the actual source graph coordinates, and the held bars use two hundred eighty pixels per normalized unit. The distance slider moves the marker along this fixed curve. The canvas illustration stays static on this deployed source; these exact numerical comparisons teach the calculator relationship without claiming orbital motion or a real mission prediction.