Geosynchronous and Geostationary Satellite Formula and Calculator for Speed, Angular Velocity and Orbit Period
The geostationary radius of orbit is specific to satellites that are positioned directly above the equator and appear stationary relative to a fixed point on Earth. The geosynchronous radius of orbit refers to satellites that have an orbital period equal to the Earth’s rotational period (24 hours), but they do not necessarily stay over the same point on the Earth’s surface.
The radius of a geosynchronous orbit is also approximately 42,164 km from the Earth's center, similar to the geostationary orbit. However, the satellite's position relative to the Earth's surface changes due to orbital inclination or eccentricity.
Based on the coverage and applications there are different types of satellites viz. international and national or domestic. For example, INTELSAT is used for international communication and DOMSAT is used for domestic communications.
Speed or velocity of satellite : The speed or velocity of a satellite in orbit is approximately 3.07 kilometers per second (km/s) or
about 7,000 miles per hour (mph). This speed is required for a satellite to maintain its orbit at an altitude of approximately
35,786 kilometers (about 22,236 miles) above the Earth's equator.
Period of Orbit (T): The period of orbit is the time it takes for the satellite to complete one orbit around the Earth.
Angular Velocity (w) : The angular velocity of the satellite is the rate at which it moves around the Earth in radians per second.
Acceleration (a) : The acceleration of the satellite can be calculated using the centripetal acceleration formula,
which is the acceleration required to keep an object in circular motion.
Orbit radius : The radius of a satellite orbit is approximately 35,786 kilometers (about 22,236 miles) above the Earth's surface.
This specific altitude is required for a satellite to have an orbital period equal to the Earth's rotation period, which is approximately 24 hours.
This calculator is useful for engineers in various fields including satellite design and development, telecommunication and network planning, antenna and ground station design, satellite operations and maintenance, satellite tracking and control, weather forecasting and earth observation, remote sensing and earth science etc.
Let us explore geosynchronous orbit calculator which performs satellite calculations such as speed or velocity, orbital period, angular velocity and acceleration using satellite radius of orbit formula.
Geosynchronous Satellite calculator
The following calculator takes satellite orbit as input and calculates all the other parameters as per equations or formulas.
Example Calculation
INPUTS:
Radius of Orbit = 41000 Km
OUTPUTS:
Velocity of satellite = 3.11 km/s
period of orbit (time of period)= 82620.29 sec
Angular velocity = 76 x 10-6 rad/sec
Acceleration = 2.5 x 10-6 km/sec*sec
Geostationary Satellite formula and calculator
• Both geostationary and geosynchronous orbits have the same orbital radius (approximately 42,164 km), geostationary orbits are a subset of geosynchronous orbits. Geostationary satellites have zero inclination and appear stationary above the equator, whereas geosynchronous satellites can have varying inclinations and appear to move relative to the Earth's surface.
Conclusion
In summary, geosynchronous satellite calculators and formulas are valuable tools for engineers in various disciplines,
enabling them to plan, design, operate, and maintain satellite systems effectively.
These calculations are essential for ensuring the successful deployment and operation of geosynchronous satellites,
which play a critical role in modern communication, broadcasting, weather monitoring, and Earth observation.
➨NOTE : The same calculator mentioned above can be used for geostationary satellite
calculations to calculate speed, angular velocity and orbit period from orbit radius as input.