Gravitational Binding Energy

Want to find out how much energy it takes to blow up a planet? This is the way to do it. Gravitational Binding Energy (often abbreviated as GBE) is defined as the amount of energy it would take to scatter the mass of a gravitationally bound body to the point that its own gravity will not pull it back together again. There are precise calculations for this via integration, but a good approximation can be achieved with the following formula:

Where U = GBE, M = the mass of the body in question, r = its radius, and G = the gravitational constant.

Ignorance of this formula often leads to vast underestimates of the energy required to destroy astronomical objects (for example, some people assume it scales linearly with mass or volume).

Please note that this formula only works on objects that are mostly held together by their own gravity (aka large objects in space such as asteroids, moons, planets, stars, etc.) It also doesn't work on black holes, for obvious reasons.

List of approximate GBE values for various objects:

Earth's moon (Luna): 1.24e29j Earth: 2.24e32j (calculated with a more accurate method than the above formula) The sun (Sol): 6.87e41j Average neutron star: 5.23e46j

SD.net's Planetary Parameter Calculator gives a simplified approach to finding a celestial body's GBE.

See also:

- Planetbusters - Starbusters