Gravity Calculator: Newton Law of Gravitation, Orbit Speed and Escape Velocity

The gravitational force between masses, and the orbit speed, period and escape speed round a planet.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

For the force between two masses enter both masses and the distance between their centres. The force is G times the product of the masses over the distance squared, with G = 6.6743 x 10^-11.

For an orbit pick a planet, moon or star, or enter your own mass and radius, and an altitude. You get the gravity at the surface and at the altitude, the speed and time of a circular orbit, and the escape speed.

The orbit speed is where gravity gives just the centripetal force. The escape speed is the square root of 2 times the surface orbit speed.

Formulas used

  • F = \frac{G m_1 m_2}{r^2}
  • v = \sqrt{\frac{GM}{r}}
  • v_{esc} = \sqrt{\frac{2GM}{R}}
  • T = 2\pi\sqrt{\frac{r^3}{GM}}

Worked example

With the default numbers in the calculator above:

  1. Gravitational acceleration at the surface: 9.8203 m/s²
  2. Gravitational acceleration at the altitude: 8.6943 m/s²
  3. Speed in a circular orbit at that altitude: 7672.6 m/s (27621 km/h)
  4. Time for one orbit: 5544.8 s (92.414 minutes)
  5. Escape speed from the surface: 11186 m/s (40270 km/h)

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want? The force between two masses.

  1. Gravitational force between the masses: 6.6743e-5 N

Common questions

Why do astronauts float?

Gravity at the space station is still about 89 percent of its value at the surface. They float because they and the station are falling together round the Earth.

What is escape velocity?

The speed needed to leave a body for good, ignoring air drag. For the Earth it is about 11.2 km/s.

Does the altitude count from the centre?

No. Enter the altitude above the surface. The calculator adds the radius.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Newton, Principia; Halliday, Resnick and Walker, Fundamentals of Physics; NASA planetary fact sheets.

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