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The circular orbital radius formula calculates the distance from the center of a celestial body to an object in circular orbit based on its orbital velocity and the gravitational parameter of the central body.
The calculator uses the formula:
Where:
Explanation: This formula derives from the balance between gravitational force and centripetal force required to maintain a circular orbit.
Details: Calculating orbit radius is essential for satellite deployment, space mission planning, and understanding orbital mechanics. It helps determine the appropriate altitude for different types of orbits (LEO, MEO, GEO).
Tips: Enter the velocity of circular orbit in meters per second. The value must be positive and valid for Earth orbit calculations.
Q1: What is Earth's gravitational constant?
A: Earth's standard gravitational parameter (GM) is 3.986004418 × 10¹⁴ m³/s², representing the product of Earth's mass and the gravitational constant.
Q2: How does orbital velocity affect orbit radius?
A: Higher orbital velocities result in smaller orbit radii, while lower velocities require larger radii to maintain stable circular orbits.
Q3: What are typical orbital velocities for Earth satellites?
A: Low Earth Orbit (LEO): ~7.8 km/s, Medium Earth Orbit (MEO): ~3.9-4.7 km/s, Geostationary Orbit (GEO): ~3.1 km/s.
Q4: Can this formula be used for other celestial bodies?
A: Yes, but you must use the appropriate gravitational parameter (GM) for the specific celestial body instead of Earth's value.
Q5: What is the relationship between orbit radius and orbital period?
A: According to Kepler's third law, orbital period increases with orbit radius (T² ∝ r³ for circular orbits).