Illustrated Physics
physics, drawn
Concept

Gravity — where it appears

The attraction between masses, described by Newton as a force falling with the inverse square of distance and by Einstein as the curvature of spacetime. Near the Earth's surface it is a nearly uniform pull of 9.8 m/s², and at larger scales it shapes every orbit.

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

The blow-out band has two edges, not one. The ratio of radiation force to gravity against grain radius, with the radiation-pressure efficiency included: a grain much smaller than the wavelength of the light barely interacts with it — the efficiency falls as the fourth power of the size, which is Rayleigh's law — so the ratio stops rising and turns over. The dashed line is the same ratio with the efficiency taken as one, which is the usual drawing and is right only to the right of the turnover at 115 nm. The consequence is that a grain can be too small to be blown out as well as too large. Taking the threshold at a half — the value at which a grain released from a circular orbit is unbound — the band runs from 48.2 nm to 574 nm, and the largest ratio any grain of this material reaches is 1.87. Everything outside that band stays, and what stays does not stay put: it spirals.

The size the light cannot blow away

Radiation pressure and gravity both fall as the inverse square of distance, so their ratio is a property of the grain and not of where it is. What follows is a band of sizes that get blown out — with a lower edge as well as an upper one — and a drag, on everything else, that is the same pressure read one order further in v/c.

astrophysics · Radiation pressure Throws that grow into orbits. The longest throws possible from one point on the Earth, at launch speeds of 3, 5, 6.5, 7.5 km/s, ignoring air, each at its best angle, drawn to scale round the Earth. 3 km/s: launched at 42.8° above the horizontal, landing 1.0 thousand km away; 5 km/s: launched at 37.8° above the horizontal, landing 3.2 thousand km away; 6.5 km/s: launched at 29.7° above the horizontal, landing 6.8 thousand km away; 7.5 km/s: launched at 17.6° above the horizontal, landing 12.2 thousand km away. The faster the throw, the flatter the best launch and the further round the Earth it lands; at the circular-orbit speed, 7.91 km/s, the best launch is horizontal and the throw never comes down.

The parabola that is the top of an ellipse

Every textbook throw is a parabola, the best angle is 45°, and the range goes as the square of the speed. All three are statements about a flat Earth with gravity pointing the same way everywhere. On the real one a throw is a piece of an orbit — an ellipse with the Earth's centre at one focus — and the parabola is what the top of that ellipse looks like when the Earth is large. Throw faster and the best angle falls, the range runs ahead of the formula, and at eight kilometres a second the best throw is horizontal and never lands.

mechanics · Projectile

Named alongside it

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

AberrationApproximationCross-sectionDissipationDustEllipseThe inverse-square lawKepler orbitOrbitOrbital speedParabolaProjectile motion

All concepts