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:
- Fc 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.