Geo Radius Given Absolute Angular Velocity of Earth Calculator

Geostationary Radius Formula:

\[ R_{gso} = \left( \frac{GM_{Earth}}{\Omega_E^2} \right)^{1/3} \]

Geostationary Radius:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Geostationary Radius?

The geostationary radius is the orbital distance from Earth's center where a satellite orbits at the same angular velocity as Earth's rotation, appearing stationary relative to a fixed point on Earth's surface.

2. How Does the Calculator Work?

The calculator uses the geostationary radius formula:

\[ R_{gso} = \left( \frac{GM_{Earth}}{\Omega_E^2} \right)^{1/3} \]

Where:

\( R_{gso} \) — Geostationary radius (meters)
\( GM_{Earth} \) — Earth's geocentric gravitational constant (3.986004418 × 10¹⁴ m³/s²)
\( \Omega_E \) — Angular speed of Earth (radians/second)

Explanation: This formula derives from balancing gravitational force with centripetal force required for circular orbit at Earth's rotational speed.

3. Importance of Geostationary Orbit Calculation

Details: Accurate geostationary radius calculation is crucial for satellite positioning, communication systems, weather monitoring, and ensuring satellites remain fixed relative to Earth's surface.

4. Using the Calculator

Tips: Enter Earth's angular speed in radians per second. The standard value is approximately 7.2921159 × 10⁻⁵ rad/s.

5. Frequently Asked Questions (FAQ)

Q1: What is the standard angular speed of Earth?
A: Earth's angular speed is approximately 7.2921159 × 10⁻⁵ radians per second, corresponding to one rotation every 23 hours, 56 minutes, and 4 seconds.

Q2: What is the approximate geostationary altitude?
A: Approximately 35,786 kilometers above Earth's equator, with a radius of about 42,164 kilometers from Earth's center.

Q3: Why is this orbit important for satellites?
A: Geostationary orbit allows satellites to maintain fixed positions relative to Earth, making them ideal for communications, broadcasting, and weather monitoring.

Q4: Does this calculation account for Earth's oblateness?
A: This basic formula assumes a spherical Earth. For precise orbital calculations, additional factors like Earth's oblateness (J₂ effect) must be considered.

Q5: Can this formula be used for other planets?
A: Yes, with appropriate values for the planet's gravitational parameter and rotational angular speed.