7.1.3 Geostationary and Other Orbits

Is it better to park a satellite at high or low altitude? Well, they both have their own pros and cons.

Low altitude

Can take higher resolution images of Earth.
Transmits and receives signals/messages with shorter delay.
Requires less fuel and cheaper to launch into orbit.

High altitude

Wider coverage because can maintain direct line of sight with a large portion of Earth’s surface at any one time
Suffers less atmospheric drag and requires less frequent orbital boosts.

Low Earth Orbits (LEO)

The majority of satellites are LEO satellites. At altitudes of only a few hundred kilometres, they have orbital periods of about 90 minutes. Famous satellites in the LEO orbits include the International Space Station (ISS) and the Hubble Telescope.

Middle Earth Orbits (MEO)

A famous occupant of the MEO space is The Global Positioning System (GPS), a constellation of >24 satellites parked at altitude of about 20,000 km. From this higher altitude, each satellite has a larger coverage area. They have orbital periods of 12 hours.

Geostationary Orbits (GEO)

While a satellite is going around the Earth, the Earth itself is also rotating. If the satellite were to “rotate” at the same rate as the Earth about the same rotational axis, it would appear stationary in the sky (to somebody on Earth).

To achieve this, the satellite must

have an orbital period of 24 hrs,
orbit in a west to east direction, and
be in the equatorial plane.

Such an orbit, called the geostationary orbit, is found at an altitude of 36,000 km.

Example

Calculate the altitude of the geostationary orbit.

Earth’s radius $=6370\text{ km}$

Earth’s mass $=5.97\times {{10}^{{24}}}\text{ kg}$

Solution

GEO satellites have orbital period of 24 hours.

$\displaystyle \omega =\frac{{2\pi }}{T}=\frac{{2\pi }}{{24\times 60\times 60}}=7.27\times {{10}^{{-5}}}\text{ rad }{{\text{s}}^{{-1}}}$

The gravitational pull provides the required centripetal force for circular motion.

$\displaystyle \begin{aligned}\frac{{GMm}}{{{{r}^{2}}}}&=mr{{\omega }^{2}}\\GM&={{r}^{3}}{{\omega }^{2}}\\(6.67\times {{10}^{{-11}}})(5.97\times {{10}^{{24}}})&={{r}^{3}}{{(7.27\times {{10}^{{-5}}})}^{2}}\\r&=42235\text{ km}\end{aligned}$

The altitude $=42235-6370=35900\text{ km}$

Since the GEO orbit is at a very high altitude, launching of GEO satellites requires very powerful and expensive rockets. Nevertheless, it is the orbit of choice for communications satellites.

Geostationary satellites stay at a fixed point above the Earth, which is convenient for communication satellites because they appear stationary when viewed from Earth (if not ground antenna will have to continuously track the satellites as they move across the sky)
Unfortunately, being constrained to the equatorial plane also means geostationary satellites cannot serve the polar regions (because from the polar regions they are below the horizon and cannot be sighted.)

Polar Orbit

A polar orbit is one that carries the satellite above or nearly above the poles. It has an inclination of 60 to 90 degrees to the equator. The main attraction of polar orbits is that they are able to “raster scan” the entire earth’s surface, including the polar regions. They are used for Earth-mapping, reconnaissance, meteorology and telecommunication.