Orbital mechanics in CALCULA
The Orbital mechanics field applies celestial mechanics: reaching orbit, changing orbit, propulsion, and locating yourself on Earth.
Staying in orbit
At a given altitude, the speed needed to stay in orbit is fixed. Counter-intuitively it decreases with distance: the ISS races along at 7.7 km/s at 400 km, a geostationary satellite at only 3.1 km/s at 35,786 km — but it takes a whole day to go round.
Example
Kepler's third law gives the Moon's period (semi-major axis 384,400 km): about 27.3 days, which is what we observe.
The delta-v bill
Delta-v is the total velocity change of a manoeuvre. The logarithm is the trap: every extra kilogram of propellant must itself be accelerated, which forces you to carry yet more. A rocket is mostly a tank.
Changing orbit and the vis-viva equation
The vis-viva equation gives the speed at any point of an elliptical orbit. A Hohmann transfer links two circular orbits by half an ellipse — the most propellant-efficient manoeuvre for large altitude changes.
Coordinates and GPS distances
CALCULA converts between decimal degrees, degrees-minutes-seconds and degrees-decimal-minutes, and computes the distance between two points on the globe (spherical formula). Five decimal places of a degree are worth about one metre.
Typing it into CALCULA
Open “≡” on “orbital mechanics”, choose the manoeuvre (reaching orbit, Kepler, Tsiolkovsky, Hohmann, vis-viva, GPS), and enter the known parameters. The visualisation draws the orbit or the trajectory. See also physics.