Gravitational Binding Energy?

📌 CONCEPT: The gravitational binding energy of a system is the energy required to separate the objects in the system to infinite distance, and it is given by the formula U = -2GM^2/r, where U is the gravitational binding energy, G is the gravitational constant, M is the mass of the system, and r is the distance between the objects.

📐 RULE / FORMULA: The gravitational binding energy of a system is directly proportional to the mass of the system and inversely proportional to the distance between the objects, i.e., U ∝ M/r.

💡 WORKED EXAMPLE: Consider two objects with masses m and M separated by a distance r. If the distance between the objects is doubled, the gravitational binding energy of the system changes as follows: U1 = -2GM^2/r and U2 = -2GM^2/2r. Comparing U1 and U2, we can see that the gravitational binding energy decreases by a factor of 2 when the distance between the objects is doubled.

⚠️ COMMON MISTAKE: Students often get confused between the gravitational binding energy and the gravitational potential energy. The gravitational binding energy is the energy required to separate the objects in the system to infinite distance, whereas the gravitational potential energy is the energy a body has due to its position in a gravitational field.