How to Calculate Orbital Period

We calculate orbital period for the celestial bodies revolving around each other. Orbital period is the time period taken by the given object to complete one revolution around another object. This orbital period of the objects is calculated using the fully defined version of Kepler’s third law. Knowing how to calculate orbital period is of great importance in understanding many of the astronomical facts.

There are several kinds of orbital periods such as, sidereal period, synodic period, draconic period, anomalistic period and the tropical period.

The formula for calculating orbital period is given as,

T = 2 π √R3

In the above formula,

  • “R” is the length of the semi-major axis
  • “μ” is the standard gravitational parameter
  • “G” is the gravitational constant between two bodies
  • “M” is the mass of the body (central body)

Kepler has formulated many laws for studying the planetary motions. These laws were formulated in 17th century and are of great importance even today. Orbital period of the planets is usually calculated in astronomical units like years. For small planets that have small orbits we calculate it in days e.g. Mercury and Moon.

  • Above formula can not only be used to calculate the orbital period of the planets but also to calculate the orbital period of moons, satellites, asteroids and comets, etc.
  • The semi-major axis of a pair of planets is the half of major axis of the planets, wherein major axis is the longest diameter that runs through the center and both the foci. In certain special cases the semi-major axis is the radius of the circular orbit. This is usually true in cases where the motion is in circular orbits instead of elliptical orbits.
  • The standard gravitational parameter is the gravitational constant and the mass of the body i.e.

μ = GM

  • G is the gravitational constant. The value of this gravitational constant is 6.67428 × 10-11 m3 kg-1 s-2.
  • “M” which is the mass of the central body is the mass of the body around which you are about to calculate the orbital period of another body which is revolving around it.
  • When you have all the above values, you can substitute these values in the above equation and calculate the orbital period.
  • To get the values of the semi-major axis and masses of the bodies, you need to refer to the astronomical tables. These tables are easily available online.
  • In case you are not getting the values for any newly discovered planets or comets, you need to determine these values through observations. It takes a lot of effort to determine these values through observations and need many observations to achieve accuracy.
  • A scientific calculator is a must to calculate the orbital period as the calculations are not so easy to be performed manually.
  • Before performing calculations, convert the units in compatible formats.

Formula for calculating orbital period when you want to consider mass of the two bodies

P = 2 π √ R3/ G (M1 + M2)

R and G in this formula are same as in the above formula. M1 is the mass of the first body while M2 is the mass of the second body.

Below are the orbital periods of the planets revolving around the sun. Here, 1 year is considered as 365 days i.e. the orbital period of Earth around the Sun.

Planet Orbital period in days Orbital period in years
Mercury 0.2408467 y 87.96926 d
Venus 0.6151973 y 224.80080 d
Earth 1.0000174 y 365.25636 d
Mars 1.8808480 y 686.97973 d
Jupiter 11.861983 y 4332.589 d
Saturn 29.457159 y 10759.227 d
Uranus 84.020473 y 30688.478 d
Neptune 164.770132 y 60182.291 d

Hope, above steps and information will help you in calculating the orbital periods of many planets, satellites and any celestial body revolving around any other body.

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