Enter the mass of the celestial body, the distance from the celestial body, and the radius of the object experiencing the force into the calculator to determine the tidal force exerted on the object.

Tidal Force Formula

The following formula is used to calculate the tidal force exerted by a celestial body on another object. 

F_t = frac{2 G M r}{d^3}

Variables:

  • Ft is the tidal force (Newtons)
  • G is the universal gravitational constant (6.67430 × 10-11 m3 kg-1 s-2)
  • M is the mass of the celestial body (kilograms)
  • r is the radius of the object experiencing the force (meters)
  • d is the distance from the center of the celestial body to the center of the object (meters)

To calculate the tidal force, multiply twice the universal gravitational constant by the mass of the celestial body and the radius of the object experiencing the force, then divide by the cube of the distance from the celestial body.

What is Tidal Force?

Tidal force is the secondary effect of the force of gravity and is responsible for the tides on Earth. It arises because the gravitational force exerted by one body on another is not constant across it; the nearest side is attracted more strongly than the farthest side. This difference in attraction creates a stretching effect on the body, which can cause it to become elongated along the axis pointing towards the celestial body causing the tidal force. This effect is most clearly observed in the Earth-Moon system but occurs in other systems as well, such as the tidal forces between a planet and its satellites.

How to Calculate Tidal Force?

The following steps outline how to calculate the tidal force.

  1. First, determine the mass of the celestial body (M) in kilograms.
  2. Next, determine the distance from the celestial body (d) in meters.
  3. Next, determine the radius of the object experiencing the force (r) in meters.
  4. Next, gather the formula from above = Ft = (2 G M r) / d3.
  5. Finally, calculate the tidal force (Ft) in Newtons.
  6. 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.

Mass of the celestial body (M) = 7.342 × 1022 kg (Moon’s mass)

Distance from the celestial body (d) = 384,400,000 m (average distance from Earth to Moon)

Radius of the object experiencing the force (r) = 6,371,000 m (Earth’s radius)