Satellites
Every satellite orbiting the Earth — from the International Space Station skimming just above the atmosphere to a weather satellite that seems to hover motionless over one spot on the equator — obeys exactly the circular-orbit physics built up across this topic. The difference between them comes down to nothing more than orbital radius.
Low Earth orbit
A satellite in low Earth orbit (LEO) travels at an altitude of only a few hundred kilometres above the Earth's surface — close enough that its orbital radius $r$ (measured from the Earth's centre) is only slightly larger than the Earth's own radius. Applying $v = \sqrt{GM/r}$ from the Circular Orbits lesson, a small orbital radius means a comparatively high orbital speed, and applying $T = 2\pi\sqrt{r^3/GM}$, it also means a short orbital period — typically around 90 minutes for a satellite a few hundred kilometres up.
- High orbital speed. LEO satellites typically travel at around 7–8 km/s relative to the Earth's centre, similar to the value calculated for a satellite at $7.00\times10^6\,\text{m}$ in the worked example of the Circular Orbits lesson.
- Short period. Completing an orbit in roughly 90 minutes means a LEO satellite circles the entire Earth around sixteen times a day.
- Typical uses. The low altitude makes LEO ideal for Earth imaging and remote sensing (fine surface detail is only possible from close range) and for crewed spaceflight, including the International Space Station, which orbits at roughly 400 km altitude.
- Ground track. Because the Earth rotates underneath a LEO satellite much more slowly than the satellite completes an orbit, the path it traces over the ground shifts with each pass — useful for scanning different strips of the Earth's surface over time, but it means a LEO satellite is never above the same ground location for long.
Geostationary orbit
A geostationary satellite is a special case chosen so that it appears to stay permanently fixed above one point on the Earth's equator. For this to happen, the satellite's orbital period must exactly match the time it takes the Earth itself to rotate once on its axis relative to the distant stars — one sidereal day, very close to 24 hours (23 hours 56 minutes, to be precise, though 24 hours is a good working approximation). If the satellite's period matched this exactly, and its orbit lay directly above the equator moving in the same direction as the Earth's rotation, it would trace out no ground track at all — it would simply sit above the same spot indefinitely.
Because orbital period and orbital radius are linked by $T^2 \propto r^3$ (from the Planetary Motion lesson, applied here to circular orbits around the Earth), fixing the period at 24 hours fixes a single, unique orbital radius. Every geostationary satellite, regardless of its mass, must orbit at this same radius.
Because a geostationary satellite appears permanently fixed in the sky as seen from the ground, a receiving dish or antenna can be pointed at it once and left in that fixed orientation, with no motorised tracking system needed to follow the satellite across the sky. This is exactly why geostationary orbit is the standard choice for communications satellites (television broadcast, some internet relay) and weather-monitoring satellites that need to continuously watch the same region of the Earth's surface — the fixed geometry massively simplifies both the ground equipment and the interpretation of continuous image sequences.
Comparing the two
- LEO satellites orbit fast, low, and with a short period, making many close passes over different parts of the Earth each day — well suited to detailed imaging and human spaceflight, but requiring tracking equipment on the ground.
- Geostationary satellites orbit at a single, far larger fixed radius with a 24-hour period matched to the Earth's own rotation, appearing stationary in the sky — ideal for continuous coverage of one region, at the cost of much lower surface resolution due to the far greater distance involved.
- Both cases are simply the same circular-orbit relations from earlier in this topic, $v = \sqrt{GM/r}$ and $T^2 \propto r^3$, applied at two very different values of $r$.
Key takeaways
- Low Earth orbit satellites orbit at a few hundred kilometres altitude, with high orbital speed (roughly 7–8 km/s) and short period (roughly 90 minutes), well suited to imaging and crewed spaceflight.
- Geostationary satellites have a period matched to the Earth's rotation (approximately 24 hours, precisely one sidereal day), so they appear fixed above one point on the equator.
- The condition $T^2 \propto r^3$ fixes a unique orbital radius for geostationary orbit, calculated here as roughly 42,000 km from the Earth's centre.
- A fixed position in the sky lets ground antennas and dishes point at a geostationary satellite without needing to track its motion, making it ideal for communications and weather monitoring.
- Both LEO and geostationary orbits are governed by exactly the same circular-orbit relations derived earlier in this topic — they differ only in orbital radius.
- This topic has built up orbital mechanics from first principles: circular orbits and the centripetal role of gravity, escape velocity as the energy threshold for leaving a gravitational field altogether, Kepler's laws describing the true elliptical motion of orbiting bodies, and finally satellites as a direct practical application of all of it.
- These same principles are not limited to artificial satellites — exactly the same physics governs the Moon's orbit around the Earth, planets orbiting stars, stars orbiting each other in binary systems, and even stars orbiting within the gravitational field of an entire galaxy, at every scale covered across this Astrophysics module.