The main types of synchronous orbits are classified by the time it takes them to complete an orbit. The adjective synchronous refers to the fact that a body orbits another (in our case, the earth) in the same direction in which the earth rotates, and this orbit takes the same time as taken by the earth to complete a full rotation.
Geosynchronous orbits
These are synchronous orbits that have the same period as the earth, which means that one full orbit is completed in 23 hours, 56 minutes, and 4 seconds (the period is not exactly equal to a day). These fall under the category of high earth orbits, with the altitude above the equator where these bodies must be placed being approximately 36000 km.
Note that the altitudes are measured relative to the equator to have a common ground for measurements as the earth is not a perfect sphere.
The objects in these orbits have the particularity that, as seen by an observer on the earth, they remain in the same place in the sky. This makes them useful for telecommunications applications.
Geostationary orbits
These are geosynchronous orbits located over the equator. Satellites in this type of orbit will, therefore, always have a view of the same part of the earth below them, which makes them especially suited for weather-monitoring systems or search and rescue beacons.
Figure 1. Geostationary and geosynchronous orbits. Source: gisgeography.com.
Find the radius of orbit and the altitude of a satellite orbiting the earth in a geostationary orbit. The earth has a mass of 5.97⋅1024 kg and a radius r of 6.37⋅106 m, and the gravitational constant G has a value of 6.67⋅10-11 Nm2kg-2.
We begin by equating the gravitational force acting on the satellite due to the earth to the equation for the centripetal acceleration:
\[\frac{G \cdot M \cdot m}{r^2} = m \cdot r \cdot \omega^2\]
Here, M is the mass of the earth, m is the mass of the satellite, r is the radius of the orbit, and ω is the angular speed. This gives us:
\[r^3 = \frac{G \cdot M}{\omega^2}\]
A geostationary satellite orbits the earth at the same angular speed as the earth rotates itself. The angular speed can be found from the time period of the earth in seconds (we know that the earth completes a full turn once a day).
\[\omega = \frac{2 \pi}{T} = \frac{2 \pi}{(3600 \cdot 23) + (60 \cdot 56) + 4} = 7.29 \cdot 10^{-5} rad/s\]
This value can be put into the equation to find r:
\[r = 4.22 \cdot 10^7 m\]
The altitude can be found by subtracting the radius of the earth from the radius of orbit, giving the altitude as:
\[h = 3.58 \cdot 10^7 m\]
Semi-synchronous orbits
These are synchronous orbits that have half the period of the earth’s rotation. One full orbit is thus completed in half a day. For this to be achieved, the bodies must be placed at an approximate distance of 20200 km, which puts them in the category of medium earth orbits.
In these orbits, bodies pass the same spot every 12 hours, which makes satellites on these orbits very useful for geolocation purposes as a particular spot can be accurately located by receiving signals every 12 hours.
Altitude classification of synchronous orbits
Orbits can also be classified by altitude in relation to the surface of the earth. There are three main types of synchronous orbits whose thresholds are not fixed.
Low earth orbits
These are close to the earth’s surface (i.e., 160 km - 1000 km) and are usually designed for satellites that gather information about the earth. Although high earth orbits do include weather-monitoring satellites, most of them are found in low earth orbits, so they can go over many different zones very quickly.
Low earth orbits are also used for communications as they are cheap to launch compared to higher orbit satellites and require less powerful transmitters. Many scientific satellites gathering information about the earth’s conditions are in this kind of orbit as the earth, and the satellites are orbiting at different angular speeds, which means that they do not stay over the same place, and the whole of the surface can be scanned. These orbits usually lie in a plane that includes the north and south pole in order to cover as much of the earth as possible.
Medium earth orbits
These are orbits like the semi-synchronous ones that usually have a specific function due to a special tuning of the radial distance to obtain a specific period and shape. Their distance ranges from 2000 km to 35786 km. There is, for instance, an orbit called Molniya, which allows satellites to observe and monitor high latitude zones very efficiently. It is, however, an elliptical orbit.
Medium earth orbits are mainly used for navigation and communications.
Figure 2. Molniya orbit. Source: earthobservatory.nasa.gov.
High earth orbits
These are orbits that are far away from the earth’s surface (i.e., 35786 km and beyond). Their main uses range from weather monitoring and safe-and-rescue beacons or telecommunications to the gathering of information about the solar system and the universe due to the lack of interference. There are, for instance, important telescopes placed on certain spots that have allowed us to thoroughly study the sun, its cycles, and its properties.
Synchronous Orbits - Key takeaways
- The closed orbits that satellites follow around the earth are usually synchronised with the rotation of the earth.
- Synchronous orbits are classified in terms of their period of rotation.
- Objects in synchronous orbits are said to be in high, medium, or low orbits, depending on their altitude with respect to the surface of the earth.
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