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Orbital period calculator

A-level Fields and space

The time for one orbit of a small mass around a much larger mass, such as a satellite around the Earth.

T = 2π√(r³ / (G M))

This free calculator is for A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.

Quantity to find

TOrbital period to find 86300 s

rOrbital radius

GGravitational constant constant N m²/kg²

MMass of the central body

Significant figures

Working

Write the equation
T = 2π√(r³ / (G M))
Constants used
G = 6.67 × 10⁻¹¹ N m²/kg²
Substitute the values
T = 2π × √((4.22 × 10⁷)³ ÷ ((6.67 × 10⁻¹¹) × (5.97 × 10²⁴)))
Calculate
T = 86317.4 s
Give the answer to 3 significant figures
T = 86300 s
In standard form: 8.63 × 10⁴ s

Worked example

Find T, the orbital period. Given: orbital radius r = 4.22 × 10⁷ m; mass of the central body M = 5.97 × 10²⁴ kg; gravitational constant G = 6.67 × 10⁻¹¹ N m²/kg².

Write the equation
T = 2π√(r³ / (G M))
Constants used
G = 6.67 × 10⁻¹¹ N m²/kg²
Substitute the values
T = 2π × √((4.22 × 10⁷)³ ÷ ((6.67 × 10⁻¹¹) × (5.97 × 10²⁴)))
Calculate
T = 86317.4 s
Give the answer to 3 significant figures
T = 86300 s
In standard form: 8.63 × 10⁴ s

Symbols and units

Symbol	Quantity	SI unit
T	Orbital period	s
r	Orbital radius	m
G	Gravitational constant (constant)	N m²/kg²
M	Mass of the central body	kg

Orbital period: rearranged

To find orbital period: T = 2π√(r³ / (G M))
To find orbital radius: r = ∛(G M T² / (4π²))
To find mass of the central body: M = 4π² r³ / (G T²)

Exam tip

r is measured from the centre of the central body. The orbital radius is the planet’s radius plus the height of the satellite.

Common questions

What is the formula for orbital period?

The equation is T = 2π√(r³ / (G M)), where T is the orbital period (s); r is the orbital radius (m); M is the mass of the central body (kg); G is the gravitational constant (N m²/kg²).

What units should I use for orbital period?

In SI units: orbital period in s, orbital radius in m, gravitational constant in N m²/kg², mass of the central body in kg. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange T = 2π√(r³ / (G M))?

Rearranging gives these forms: to find orbital period: T = 2π√(r³ / (G M)). to find orbital radius: r = ∛(G M T² / (4π²)). to find mass of the central body: M = 4π² r³ / (G T²).

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Read the full explanation on the Orbital period of a circular orbit formula page. More fields and space equations: Coulomb’s law, Uniform electric field, Electric field strength, Field of a point charge, Newton’s law of gravitation, Gravitational field strength, Gravitational potential, Escape velocity. See the full list on the a-level physics equation calculator page.