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Define the term orbital velocity and the quantitative and qualitative relationship between orbital velocity, the gravitational constant, mass of the central body, mass of the satellite and the radius of the orbit using Kepler’s Law of Periods
- Orbital Velocity: The instantaneous speed and direction of an object in circular motion along its path.
- For uniform circular motion, the magnitude of the orbital velocity is constant and inversely proportional to period of the orbit:
- Law of Periods: The third of Kepler’s three laws of planetary motion, which states that the square of the orbital period of a planet is proportional to the cube of its mean distance from the Sun:
- If the above expression for orbital velocity is substituted into Kepler’s Law of Periods, then a formula for orbital velocity is produced that is specific to a satellite:
- For the case of a satellite orbiting the Earth, the formula becomes:
- From this formula, altitude is the only variable that determines the orbital velocity required for a specific orbit.
- The greater the radius of the orbit, the lower the required orbital velocity.