Gravitational binding energy is the energy needed to completely disperse a celestial body. If GBE is broken, the particles of the body will not reform or be bound to each other's gravity, but instead drift off infinitely in the direction they were moved towards. There are precise calculations for this via integration, but a good approximation can be achieved with the following formula:
Where U = GBE in joules, M = the mass of the body in question in kilograms, r = its radius in meters, and G = the gravitational constant of 6.67408x10^-11.
For stars, however, the formula is slightly different:
U is GBE in joules, G is the gravitational constant of 6.67408x10^-11, M is mass in kilograms, r is radius in meters, and n is the polytropic value attributed to the type of star. While this formula is not perfectly accurate, it is widely applicable, and is still within the acceptable margin for error.
Ignoring 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 (meaning: 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: 2.487e32J (Calculated with a more accurate method than the above formula)
- OTS 44: 6.906e37J
- VB 10: 3.139e40J
- The sun (Sol): 5.693e41J
- Rigel A: 3.817e42J
SD.net's Planetary Parameter Calculator gives a simplified approach to finding a celestial body's GBE.