How do we calculate an Earth satellite orbit?

How do we calculate an Earth satellite orbit?
Credit: NASA



Orbit type

There are three main types of Earth orbits: high, medium, and low. High Earth orbits are the farthest away from the surface, and are typically used for weather and some communications satellites. Medium Earth orbits are in between high and low orbits, and are used for navigation and specialty satellites. Low Earth orbits are the closest to the surface, and are used for most scientific satellites, including NASA's Earth Observing System fleet.
The type of orbit that is chosen for a satellite depends on its purpose. For example, weather satellites need to be able to see a large area, so they are often placed in high orbits. Communications satellites need to be able to reach a wide area, so they are often placed in medium orbits. Scientific satellites often need to be able to take detailed images of the Earth, so they are often placed in low orbits. The choice of orbit is a complex decision that must be made based on the specific needs of the satellite mission. By considering all of the factors involved, engineers can select the orbit that will provide the best performance for the mission.

How do we calculate an Earth satellite orbit?
  • Low Earth orbit (LEO): This is the closest type of orbit to Earth, ranging from 160 to 2,000 kilometers above the surface. LEO satellites are used for a variety of purposes, including weather forecasting, communications, and surveillance.
  • Medium Earth orbit (MEO): This type of orbit ranges from 2,000 to 35,786 kilometers above Earth. MEO satellites are used for a variety of purposes, including navigation, communications, and scientific research.
  • Geosynchronous orbit (GEO): This type of orbit is located 35,786 kilometers above Earth's equator. GEO satellites appear to be stationary in the sky, which makes them ideal for communications and broadcasting.
Also, based on the shape and direction of an orbit, there are many different types of orbits that can be created.


How do we calculate an Earth satellite orbit?
Credit: NASA


The shape of an orbit can be described as elliptical, circular, or hyperbolic. An elliptical orbit is characterized by two foci, with the satellite moving in an oval-shaped path around the central body. A circular orbit is characterized by the satellite moving in a circle around the central body. A hyperbolic orbit is characterized by the satellite moving in a path that takes it away from the central body.

How do we calculate an Earth satellite orbit?
Credit: NASA

Orbit calculation for Geostationary satellite

A geostationary satellite is a satellite that orbits Earth at a constant altitude of approximately 35,786 kilometers (22,236 miles) above the equator. This altitude is known as the geosynchronous equatorial orbit (GEO). Geostationary satellites appear to be stationary in the sky, which makes them ideal for communications and broadcasting.
The orbital velocity of a geostationary satellite is equal to the Earth's rotational velocity. The Earth's rotational velocity is approximately 1670 kilometers per hour (1040 miles per hour) at the equator. Therefore, the orbital velocity of a geostationary satellite is also approximately 1670 kilometers per hour (1040 miles per hour).
The orbital period of a geostationary satellite is equal to the Earth's rotational period. The Earth's rotational period is approximately 24 hours. Therefore, the orbital period of a geostationary satellite is also approximately 24 hours.
The equations for orbital velocity and orbital period can be used to calculate the orbit of any geostationary satellite. By knowing the altitude of the satellite, it is possible to calculate the orbital velocity and orbital period of the satellite. The orbital velocity and orbital period can then be used to predict the path of the satellite through space.
How do we calculate an Earth satellite orbit?

We need to ask some questions here: Why is the height of a geostationary satellite fixed?
Let's ignore the effects of all other planes and only consider the Earth and the satellite. In this case, the gravitational force is equal to the centripetal force.

How do we calculate an Earth satellite orbit?
Orbit calculation

Where:

  • T is the orbital period of the satellite in seconds
  • π is a mathematical constant that is equal to approximately 3.14
  • R is the radius of the Earth, which is equal to 6.37 × 10^6 m (r = R+h)
  • h is the altitude of the satellite above the Earth's surface, in meters
  • G is the gravitational constant, which is equal to 6.67 × 10^-11 N m^2 / kg^2
  • M is the mass of the Earth, which is equal to 5.97 × 10^24 kg

The centripetal force is the force that keeps the satellite in orbit around the Earth. The gravitational force is the force that attracts the satellite to the Earth. We can assume that the satellite is moving at a constant speed, so the centripetal force is equal to the gravitational force. Also, because V=w*R, so we can get (here r = R + h) :
geostationary  orbit

If we let T = 24 hours, and calculate 
geostationary  orbit

The calculated results show that the geostationary satellites  maintain a constant altitude of approximately 35,840 kilometers and a velocity of 3.07 kilometers per second.

In general, for circular orbits, once the orbital period is determined, the altitude of the satellite can be determined. You can also determine the orbital period if you know the height of the satellite. Try this, for a Starlink satellite, let h = 600Km, and calculate its orbit period.

To learn more about how to define an orbit, please see the 'Six Keplerian elements needed to define an orbit' in the reference section.

Reference
Six Keplerian elements needed to define the orbit
















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