Enter the semi-major axis of an object's orbit around Earth to calculate the orbit time. The calculator will provide the time it takes for one complete orbit in minutes.
Orbit Time Formula
The following formula is used to calculate the orbit time:
T = 2π * √(a³ / (G * M))
Variables:
- T is the orbit time (seconds)
- a is the semi-major axis of the orbit (meters)
- G is the gravitational constant (6.67430 × 10^-11 m³ kg^-1 s^-2)
- M is the mass of the Earth (5.972 × 10^24 kg)
To calculate the orbit time, use the semi-major axis to find the period of the orbit using Kepler's third law, which relates the time of one orbit to the size of the orbit's semi-major axis.
What is Orbit Time?
Orbit time, also known as the orbital period, is the time taken for a satellite or celestial body to make one complete orbit around another body. This time depends on the distance of the object from the body it is orbiting and the mass of the body being orbited. In the case of satellites orbiting Earth, the orbit time is determined by the semi-major axis of the orbit and Earth's mass.
How to Calculate Orbit Time?
The following steps outline how to calculate the Orbit Time.
- First, determine the semi-major axis of the orbit (a) in kilometers.
- Convert the semi-major axis from kilometers to meters by multiplying by 1,000.
- Use the formula T = 2π * √(a³ / (G * M)) to calculate the orbit time in seconds.
- Convert the orbit time from seconds to minutes by dividing by 60.
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem:
Use the following variables as an example problem to test your knowledge.
Semi-major axis of the orbit (a) = 42,164 km
Using the formula, the orbit time (T) is calculated as follows:
T = 2π * √((42,164,000 m)³ / (6.67430 × 10^-11 m³ kg^-1 s^-2 * 5.972 × 10^24 kg))
Convert the result to minutes to find the orbit time.
