The Potential Energy of Gravity calculator computes the potential energy in a two mass (m1 and m2) system separated by a specified distance (r) from the center of masses. It is typically used when calculating the Potential Energy of Gravity due to celestial bodies.
INSTRUCTIONS: Choose units and enter the following:
Potential Energy of Gravity (UG): The energy is returned in joules. However, this can be automatically converted to compatible units via the pull-down menu.
The Potential Energy of Gravity is originally derived from the equation for the Force of Gravity:
Then, physics tells us that work is the integral of force. So by the relation of `W=intFdx` we can get a work value of:
Lastly, if we specifically look at the Potential Energy of gravity and we use the knowledge that `PE=-W` then we can substitute our equation for Work for Potential Energy. But if we think a little more we realize that the original force of gravity equation is used for gravity anywhere in the solar system. Since we want to know the force of gravity relative to our earth, then `r_1` is essentially at a length of infinity. Since `r_1` is under a fraction, then `r_1 = 0` so we are left with:
`PE = -((G*M*m)/r)`
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 (ua), Light Seconds, Minutes, Hours, Days and Years, Parsecs, Kilo-Parsecs and Kilo-Light Years.