Earth Gravity Angular Rotation Rate

The Earth Gravity Equivalent Rotation Ratecalculator compute the space station rotation rate necessary for a rotating space station of a given radius (r) to have the a centripetal force matching the gravitational force of the Earth.

INSTRUCTIONS: Choose units and enter the following:

• (r) Radius of the Space Station

Rotation Rate(w):  The calculator returns the rotation rate in revs per second.  However, this can be automatically converted to compatible units via the pull-down menu.

Related Calculators:

• Compute the rotation rate for artificial gravity
• Compute the tangential velocity for artificial gravity

The Math / Science

The formula for the station rotation rate to match Earth's gravity is:

        `w = sqrt( (G*M_e * r)/D_e^2)  * (1 rev)/(2pir)`

where:

• w is the rotation rate to match Earth's gravity
• G is the Universal Gravitational Constant is 6.67384E-11 m³/kg•sec². 
• Me is the mass of the Earth
• De is the radius of the Earth
• r is the radius of the spinning space station.

This formula is the result of equating the formula for centripetal force to the force of gravity.

The formula for centripetal force is:

  `Fc=(m∙|v|^2)/r`

where:

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

The Force of Gravity equation is as follows:

         F = (G•m1•m2)/D²

where:

• F is the force of gravity
• G is the Universal Gravitational Constant is 6.67384E-11 m³/kg•sec².  
• m1 is the mass of the first object
• m2 is the mass of the second object
• D is the distance between them.