The Gravitational Radius calculator computes the distance between two masses based on the force of gravity and the  Universal Gravitational Constant.

INSTRUCTIONS: Choose units and enter the following:

• (M₁) Mass of object 1
• (M₂) Mass of object 2
• (F) Force of Gravity

Gravitational Radius (R): The gravity radius is returned in meters.   However, this can be automatically converted to other distance units (e.g. astronomical units) via the pull-down menu.

Note: vCalc provides special mass and distance units for application in space sciences.  The mass units include Earth Mass, Jupiter Mass and Solar Mass.  The distances include Astronomical Units (au), Light Seconds, Minutes, Hours, Days and Years, Parsecs, Kilo-Parsecs and Kilo-Light Years. 

The Science

The Force of Gravity equation computes the gravitational force between two masses.  In this equation, the masses are treated as point masses separated by a specified distance (Gravity Radius). The Force of Gravity equation is as follows:

         F = (G•m1•m2)/R²

where:

• F = force of gravity
• G = Universal Gravitational Constant is 6.67384E-11 m³/kg•sec².  
• m1 = mass of the first object
• m2 = mass of the second object
• R= Radius associated with a force of gravity between two masses

The Gravity Radius Calculator uses the above formula solved for R as follows:

     `R = sqrt( (G*m1*m2)/F)`

where:

• R = Radius associated with a force of gravity between two masses

Reference

• http://en.wikipedia.org/wiki/Gravitation
• http://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation