Quick questions on Orbital motion and satellites explained: HSC Physics Module 5

For a satellite of mass $m$ orbiting a central body of mass $M$ at radius $r$:

$$T = \frac{2 \pi r}{v} = 2 \pi \sqrt{\frac{r^3}{G M}}$$

Low Earth Orbit (LEO). Altitude 200 to 2000 km. Periods 90 to 130 minutes. Used by the ISS, Earth-observation satellites, and Starlink. High orbital speed (about 7 to 8 km/s).

A satellite in orbit is constantly falling toward Earth, but its tangential velocity carries it sideways fast enough that it falls "around" the curvature of Earth rather than into it. The orbit is the geometric path where gravitational acceleration matches the centripetal requirement at every instant.

In low orbits (below about $400$ km), residual atmosphere creates drag, slowly reducing orbital energy. Satellites must boost periodically (the ISS does this every few months) or eventually re-enter.

Altitude 200 to 2000 km. Periods 90 to 130 minutes. Used by the ISS, Earth-observation satellites, and Starlink. High orbital speed (about 7 to 8 km/s).

Altitude about 35 800 km (radius $4.22 \times 10^7$ m). Period exactly one sidereal day (about 23 h 56 min). The satellite sits over a fixed equatorial point.

Altitude 2 000 to 35 800 km. Used by GPS satellites (about 20 200 km altitude, 12-hour period).

$r$ is measured from the centre of Earth. For a $400$ km altitude orbit: $r = 6370 + 400 = 6770$ km.

Higher orbit means slower speed but longer period. Both period and orbital radius increase together, by $T^2 \propto r^3$.

A geostationary orbit must be equatorial and prograde. A polar orbit cannot be geostationary.

Geosynchronous orbits have a 24-hour period but may be inclined to the equator. Geostationary is a special case in the equatorial plane.