Orbits, satellites and space debris

G5.6 G3.7 G4.5 G4.6

By the end of this lesson you should be able to

Investigate the relationship between orbital radius and mass for orbiting objects using a simulation. G5.6
Solve problems involving the third law of planetary motion using T_a^2/r_a3 = T_b^2/r_b3 = 4π^2/(GM). G3.7
Consider the international collaboration required to monitor the orbits of satellites, and the management of space debris. G4.5
Consider the factors that contribute to positioning of satellites used for observation of weather, natural phenomena, traffic and military movements. G4.6

Key ideas

Gravity provides the centripetal force for an orbit; orbital speed and period depend on the central mass and the radius, not the satellite's mass.
Low Earth orbit (a few hundred km up, period ≈ 90 min): imaging, ISS. Geostationary (≈ 36 000 km up, period 24 h, above the equator): stays above one point, used for communications and weather.
Choosing an orbit trades coverage, resolution, revisit time and launch cost.
Thousands of satellites and debris fragments are tracked internationally to avoid collisions.

Key formulas (QCAA formula book notation)

\[ v = \sqrt{\frac{G M}{r}} \]

\[ T = 2\pi\sqrt{\frac{r^3}{G M}} \]

Worked example

Find the orbital radius of a geostationary satellite (T = 86 400 s).

\(r = \sqrt[3]{\frac{G M T^2}{4\pi^2}} = \sqrt[3]{\frac{(6.67\times10^{-11})(5.97\times10^{24})(86400)^2}{4\pi^2}} = 4.22\times10^7\) m

Common mistakes