Apparent Weight at the Equator

The Apparent Weight at the Equator calculator computes the weight of an object on Earth's Equator taking into account the force of gravity pulling the mass down and the centrifugal force from the Earth's rotation pushing outward.

INSTRUCTIONS: Choose units and enter the following:

• (m)  Mass of Object on Equator

Weight on Equator (w): The calculator returns the weight as total downward force in Newtons.  However, this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

The Apparent Weight at the Equator calculator computes the magnitude of the apparent weight of a mass located at the equator.  The formula for the apparent weight on the Equator is:

     `w =  m * (g - (v^2/(RE)))`

where:

• w = weight on the Equator
• m = mass of the object
• g = acceleration due to gravity. 
• v = rotational velocity of a point on the surface of the Earth at the equator

Derivation

A body at the equator is affected by the force of gravity due to the Earth's mass and by the centrifugal force due to the Earth rotating, the same force that causes the bulge in the Earth at the equator.

The true weight of a mass, m, at any point on the Earth's surface, ignoring the Earth's rotation, is the downward force of gravity which will be:

`w_0 = G*m_E*m/R_E^2`

where:

• w₀ = Force of gravity
• G = Universal Gravitational Constant is 6.67384E-11 m³/kg•sec².  
• m_E = mass of the Earth
• m = mass of the second object
• R = distance between them 

However, the mass located at the equator is also moving in a circle of radius `R_E` at speed v, so the apparent weight, w, is less than the true weight the mass would otherwise experience at the poles.

The velocity, v, of a point at the equator is given by:

      v = 2π * R_E/ Day_Sidereal

The formula for centrifugal force is:

`F_c = (m • |v|^2)/r`

where:

• F_c is the centrifugal force
• m is the mass of the object
• v is the velocity of the object
• r is the radius of the circular motion

Example of a Man

This author weighs 200 pounds.  This equates to 90.718474 kilogram on the surface of the Earth at the mean radius without Earth rotation.  On the Equator, a very accurate scale would measure a weight of 199.3083 pounds (pound force) which equals 886.5675 Newtons.