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The shapegravity. Mass changes the geometry.
FIELD IN MOTION
An illustrative lattice curves around the Sun and planets. Physical readings and a text explanation are available in About this model.
The mesh illustrates how mass influences spacetime geometry. Warping and body sizes are exaggerated, and orbital distances and mass differences are compressed. It is not a calculated spacetime metric. Select a body to read its physical mass and surface gravity, and adjust its hypothetical mass.
Illustrated influence WEAKER ⟶ STRONGER
LATTICE LINES 243
BODIES 9
EXAGGERATION 1.0× Spatial lattice Gravity well
↺ ⛶
SURFACE GRAVITY 274.2 m/s²
SCHWARZSCHILD RADIUS 2.95 km
ⓘ An exaggerated illustration of geometry. Not a literal fabric or a spacetime metric.
The interactive drawing is unavailable. The controls still provide physical readings; "About this model" explains the illustration.
Enable JavaScript for the interactive drawing. General relativity describes gravity through curved spacetime. This illustration exaggerates geometry and does not solve Einstein's field equations.
SHAPE THE FIELD
Start with a world ☉ Sun Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune 1.988 × 10³⁰ kg OUR CENTRAL STAR
Change its mass 1.00×
0.1× Actual mass ↺ 5×
More mass, a stronger illustrated bend.
About this model Reset experiment
PLAYBACK SPEED 0.1 years / sec 0.5 years / sec 1 year / sec 5 years / sec
Mass changesthe geometry. In general relativity, mass and energy influence spacetime geometry. Freely falling objects follow geodesics: the straightest possible paths through that geometry.
Read the picture as an analogy The spatial lattice is a smooth, bounded deformation towards the bodies. The gravity-well view uses a softened potential-like surface. Neither is a calculated spacetime metric or an embedding of the Solar System's actual geometry. There is no physical mesh, downward pull, or material sheet in space.
Sizes are enlarged, orbital distances use a square-root scale, and mass differences are compressed so planets' effects remain visible beside the Sun. Blue-to-gold colour indicates the strength of the illustrated influence, with no physical units. "Undeformed grid" removes only the drawing's warp; it does not switch gravity off.
What the controls calculate Each mass slider multiplies that body's reference mass while holding its mean radius fixed. The readings use g = GM/R² and rₛ = 2GM/c² . Two more come straight from general relativity: starlight grazing the body's edge is turned through 4GM/c²R , and a clock on its surface runs slow by the factor √(1 − rₛ/R) . For the Sun that is 1.75 arcseconds, the bending Eddington's expeditions measured at the 1919 eclipse, and about 67 seconds a year. For Earth the clock difference is about 22 milliseconds a year, small but large enough that GPS satellites must correct for it. Surface gravity assumes an isolated spherical body without rotation. The Schwarzschild radius is a characteristic length: these bodies are much larger than that radius and are not black holes.
Planets follow prescribed Keplerian orbits from fixed J2000 elements. Increasing the Sun's mass increases the displayed orbital rate by its square root. Changes to other planets affect the drawing and their readings, not orbital paths. There is no numerical solution of Einstein's equations, mutual planetary perturbations, or relativistic precession. Elapsed time is illustrative, not a calendar date.
Readings at the currently chosen masses Body Mass factor Gravity (m/s²) rₛ (m) Light bent (″) Clock lag (s/yr)
Planet imagery: Mercury, NASA / JHUAPL / Carnegie (MESSENGER); Venus, NASA / JPL (Mariner 10); Earth, NASA / Apollo 17; Mars, ESA / Rosetta OSIRIS, CC BY-SA 3.0 IGO; Jupiter, NASA / New Horizons; Uranus and Neptune, NASA / JPL (Voyager 2). The Sun and Saturn use schematic shading.
Sources and further reading: JPL · Planetary physical parameters ↗ JPL · Approximate planetary positions ↗ NASA · Sun fact sheet ↗ NASA · Testing general relativity ↗ Einstein Online · Geometric gravity ↗
Focus the scene with Tab, then use:
Arrow keys Rotate the camera + / − Zoom in / out Space Play / pause all motion [ / ] Step one model year Home Reset the camera ? Open these shortcuts All controls work with Tab and the arrow keys. Reduced-motion preferences start the simulation paused and turn off camera orbit.