Illustrated Physics
physics, drawn
Concept

Gravitational potential — where it appears

The gravitational energy per unit mass at a point, whose slope gives the gravitational field there. Near a point mass in three dimensions it falls as one over the distance; in two dimensions it grows as the logarithm, and clocks run slower where it is lower.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

The tick an elliptical orbit adds to a clock. The periodic part of the time a satellite clock gains or loses against one on the ground, after its constant rate offset is removed, against hours from closest approach, for the two Galileo satellites stranded in 2014 on orbits of eccentricity 0.156 and period 12.9 hours, a GPS satellite at 0.01 and a Galileo satellite on its intended near-circular orbit. The stranded satellites' clocks run ahead and behind by ±367 ns every orbit: slow near closest approach, where they are deepest and fastest, fast near the far point. A GPS clock wobbles by ±23 ns, and a satellite on a circular orbit by almost nothing. The wobble is −2√(GMa) e sin E/c², fixed by the orbit alone, which is what makes it a test.

The satellites launched into the wrong orbit

In August 2014 two European navigation satellites were left on the wrong orbit by a frozen fuel line in their rocket's upper stage: an ellipse instead of a circle. For navigation they were nearly useless. For relativity they were a gift. A clock on an elliptical orbit dips deeper into the Earth's gravity and speeds up as it falls, then climbs and slows, and both effects make it lose time near the bottom of the ellipse and gain it back near the top — a wobble of 367 nanoseconds every 12.9 hours, set by the orbit alone. Watching that wobble for three years checked the gravitational slowing of clocks five times more closely than anything had in the forty years before.

relativity · Time dilation The orbit a stretched sheet draws. A ball released sideways on a stretched elastic sheet dimpled by a central weight, at three-quarters of the speed for a circular orbit, seen from above, integrated from the exact equation of motion for a frictionless ball on the surface. A sheet under a point load sags logarithmically, which gives a force falling as 1/r, not 1/r², and the orbit is a rosette whose closest approaches come 131° apart, near the 127° of a 1/r force, never an ellipse. The demonstration shows orbits; it does not show Kepler's.

The sheet that cannot keep Kepler's orbits

A stretched elastic sheet with a heavy ball in the middle is the most popular picture of gravity there is: marbles roll round the dip like planets round a star. But a sheet pulled down by a point load sags as the logarithm of the distance, which is the potential of gravity in two dimensions, not three. Its marbles feel a force falling as 1/r, trace rosettes whose closest approaches are 127° apart instead of ellipses, and take a period proportional to their radius. The surface that does draw Kepler's orbits is a funnel shaped as −1/r, and only where it is shallow.

astrophysics · Orbit stability

Named alongside it

The objects these essays reach for when they reach for this one.

Apsidal angleAtomic clockBertrands theoremCentral forceEccentricityEquivalence principleGravitational redshiftKepler orbitKeplers third lawMembraneSatellite navigationTime dilation

All concepts