Chapter 9 — Key Takeaways (Orbit Types and Their Uses)

A one-page reference for choosing and characterizing Earth orbits. Every number here is computed from just three relations you already own: $v_{\text{circ}}=\sqrt{\mu/r}$, $T=2\pi\sqrt{a^3/\mu}$, and vis-viva.

The orbit catalog at a glance

Regime Altitude Period Typical inclination Signature use Key trait
LEO $160$–$2{,}000\ \text{km}$ $90$–$100\ \text{min}$ any ($28^\circ$–$98^\circ$) imaging, ISS, broadband cheapest, closest, self-cleaning (drag)
MEO $2{,}000$–$35{,}786\ \text{km}$ hours (GPS $\approx 12\ \text{h}$) $\sim 55^\circ$ navigation (GPS/Galileo) few satellites see the whole globe
GEO $35{,}786\ \text{km}$ $1$ sidereal day $0^\circ$ (equatorial) comms, weather hangs fixed over one longitude
HEO / Molniya perigee low, apogee $\sim 40{,}000\ \text{km}$ Molniya $\approx 12\ \text{h}$ $63.4^\circ$ high-latitude comms dwells over the north at apogee
SSO (polar) $\sim 600$–$800\ \text{km}$ $\sim 100\ \text{min}$ $\sim 98^\circ$ Earth observation constant local lighting on every pass

Equations (all reused from Chapters 6 and 8)

Quantity Relation Symbols & units
Circular speed $v_{\text{circ}} = \sqrt{\mu/r}$ $\mu$ (km³/s²), $r$ radius (km) → $v$ (km/s)
Period $T = 2\pi\sqrt{a^3/\mu}$ $a$ semi-major axis (km) → $T$ (s)
Altitude from period $a = \left(\mu T^2 / 4\pi^2\right)^{1/3}$ invert Kepler's third law
Speed anywhere (vis-viva) $v = \sqrt{\mu\left(\tfrac{2}{r}-\tfrac{1}{a}\right)}$ any conic; $r$ = current radius
Eccentricity from apsides $e = \dfrac{r_a-r_p}{r_a+r_p}$ $r_p,r_a$ = perigee/apogee radii
Apsides from $a,e$ $r_p=a(1-e),\quad r_a=a(1+e)$
Horizon coverage half-angle $\lambda = \arccos\!\big(R/(R+h)\big)$ how much of Earth a satellite at altitude $h$ sees

Numbers worth memorizing

Quantity Value
Earth $\mu$ $3.986\times10^{5}\ \text{km}^3/\text{s}^2$
Earth radius (mean / equatorial) $6{,}371\ \text{km}$ / $6{,}378\ \text{km}$
Sidereal day / solar day $86{,}164\ \text{s}$ / $86{,}400\ \text{s}$ (differ by ~4 min)
GEO radius / altitude / speed $42{,}164\ \text{km}$ / $35{,}786\ \text{km}$ / $3.07\ \text{km/s}$
GPS altitude / period / speed $\approx 20{,}200\ \text{km}$ / $\approx 12\ \text{h}$ / $3.87\ \text{km/s}$
LEO ($400\ \text{km}$) speed / period $7.67\ \text{km/s}$ / $92\ \text{min}$ (~15.6 orbits/day)
Molniya period $\approx 12\ \text{h}$, $i=63.4^\circ$, $e\approx 0.74$, apogee $\sim 40{,}000\ \text{km}$
Sun-synchronous $i\approx 98^\circ$, plane precesses $0.9856^\circ$/day
GTO → GEO circularization $\approx 1.5\ \text{km/s}$
GEO → graveyard disposal $\approx 11\ \text{m/s}$

Which orbit? A decision aid

If the mission must… Choose Because
photograph fine detail / move data with low delay LEO closest → best resolution and lowest latency (needs a constellation for coverage)
be seen globally by cheap receivers, few satellites MEO wide footprint → ~24 satellites give 4-in-view everywhere
hover over one region for a fixed antenna GEO one-day period → appears motionless over a longitude
serve high latitudes / the far north Molniya / HEO apogee dwell puts a satellite high over the pole where GEO can't reach
map the whole Earth under identical lighting Sun-synchronous near-polar reach + plane precesses once/year → constant local time

Definitions (first-defined in this chapter)

  • LEO — low Earth orbit, ~$160$–$2{,}000\ \text{km}$.
  • MEO — medium Earth orbit, between LEO and GEO; home of navigation constellations.
  • GEO — geostationary orbit: circular, equatorial, one-sidereal-day period; appears fixed in the sky.
  • GTO — geostationary transfer orbit: ellipse with LEO perigee and GEO-altitude apogee.
  • HEO — highly elliptical orbit: low perigee, very high apogee; loiters near apogee.
  • Molniya orbit — HEO with half-sidereal-day period, $i=63.4^\circ$, apogee over the northern hemisphere.
  • Sun-synchronous orbit (SSO) — near-polar LEO whose plane precesses once per year for constant lighting.
  • Polar orbit — inclination near $90^\circ$; overflies the whole globe.
  • Graveyard orbit — disposal orbit a few hundred km above GEO for retired satellites.

Common pitfalls

  • Radius vs. altitude. Speed and period use the radius ($R+h$), not the altitude. (GEO $v=\sqrt{\mu/42{,}164}$, not $\sqrt{\mu/35{,}786}$.)
  • Sidereal vs. solar day. GEO uses $86{,}164\ \text{s}$; using $86{,}400\ \text{s}$ puts you ~$77\ \text{km}$ too high and drifting.
  • "Higher = faster." Backwards. Higher is slower ($v_{\text{circ}}$ falls with $r$).
  • Polar $\ne$ sun-synchronous. Polar buys reach; sun-synchronous additionally buys constant lighting (and is slightly retrograde, ~$98^\circ$).
  • "Just use GEO." GEO is useless for high resolution, adds ~$0.25\ \text{s}$ latency, can't serve the poles, and its slots are scarce.

Mission Design / astrotools additions

  • Decision recorded: your mission's Orbit Selection block — altitude (or perigee/apogee), inclination, period, and a one-line requirement→orbit justification.
  • Track A → GEO ($35{,}786\ \text{km}$, $0^\circ$); Track B → low lunar orbit ($\sim 100\ \text{km}$, $v=1.63\ \text{km/s}$); Track C → low Mars science orbit ($\sim 400\ \text{km}$, $v=3.36\ \text{km/s}$); Track D → heliocentric orbit matched to the target asteroid.
  • astrotools: orbit_catalog.py — a helper tabulating the LEO/SSO/MEO/GEO regimes with a circular_period_min(alt_km) function to sanity-check any altitude. (Convenience helper, not a canonical module — keep orbits.py from Chapter 6 as the workhorse.)

Next: Chapter 10 — now that we know the destinations, we learn to move between them: the Hohmann transfer, plane changes, and rendezvous.