Astronomy

Mercury’s three-to-two rhythm

Track a surface meridian over two eccentric orbits. Change the spin ratio and see why Mercury presents alternating faces at successive perihelia.

Actual application image

The model and its limits

Kepler orbit with a prescribed spin ratio; no tidal capture dynamics. The planet is enlarged and the solar-day formula uses mean rates.

Equations used in the module

Equations
θ_spin = (3/2)M; P_solar = P_orbit/|ω/n - 1|

Astronomy

Lower a spacecraft’s periapsis into a thin atmosphere. Compare drag energy loss and peak heating along an idealized grazing pass.

Astronomy

Change the mass ratio. Both stars orbit their common centre of mass; compare their speeds and see the brighter star’s reflex motion.

Astronomy

Follow a climber from the equator past geostationary altitude. Compare inward gravity and outward centrifugal acceleration along the cable.