Geosynchronous and Geostationary Satellite Formulas and Calculator

This article explains the formulas and provides a calculator for determining the speed, angular velocity, and orbital period of geosynchronous and geostationary satellites.

The geostationary radius of orbit is specific to satellites positioned directly above the equator. These satellites appear stationary from a fixed point on Earth.

The geosynchronous radius of orbit applies to satellites with an orbital period equal to the Earth’s rotational period (24 hours). However, they don’t necessarily stay over the same point on the Earth’s surface. The radius of a geosynchronous orbit is approximately 42,164 km from the Earth’s center, similar to the geostationary orbit. The satellite’s position changes relative to the Earth’s surface due to orbital inclination or eccentricity. There are various types of satellites, such as international (e.g., INTELSAT) and national/domestic (e.g., DOMSAT), based on their coverage and applications.

Key Parameters

• Speed or Velocity of Satellite: 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 time it takes for the satellite to complete one orbit around the Earth.
• Angular Velocity (ω): The rate at which the satellite moves around the Earth in radians per second.
• Acceleration (a): Calculated using the centripetal acceleration formula, which represents the acceleration required to maintain circular motion.
• Orbit Radius: Approximately 35,786 kilometers (about 22,236 miles) above the Earth’s surface for an orbital period equal to the Earth’s rotation period (approximately 24 hours).

Applications

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

Geosynchronous Satellite Calculator

The calculator takes the satellite orbit radius as input and calculates parameters like speed/velocity, orbital period, angular velocity, and acceleration.

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/sec²

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

Geosynchronous satellite calculators and formulas are valuable tools for engineers in various disciplines. They enable effective planning, design, operation, and maintenance of satellite systems. These calculations are essential for the successful deployment and operation of geosynchronous satellites, which are critical for modern communication, broadcasting, weather monitoring, and Earth observation.

Note: The same calculator mentioned above can be used for geostationary satellite calculations to determine speed, angular velocity, and orbit period from the orbit radius as input.