Gravitational Binding Energy Effect

📌 CONCEPT: Gravitational binding energy is the energy required to move an object from the surface of a planet to an infinite distance, where it is no longer bound by the planet's gravity. This energy is equal to the negative change in potential energy of the object as it escapes the planet's gravitational pull.

📐 RULE / FORMULA: The gravitational binding energy (E) is given by the formula E = -GMm / r, where G is the gravitational constant, M is the mass of the planet (earth), m is the mass of the object (spaceship), and r is the radius of the planet.

💡 WORKED EXAMPLE: To calculate the percentage decrease in the earth's mass, we first need to find the gravitational binding energy using the given formula. Given that M = 5.98 × 10^24 kg, G = 6.67 × 10^-11 N m^2 kg^-2, m = 10^4 kg, and r = 6400 km = 6.4 × 10^6 m, we can plug these values into the formula to get E = - (6.67 × 10^-11) × (5.98 × 10^24) × (10^4) / (6.4 × 10^6) = -6.15 × 10^10 J.

⚠️ COMMON MISTAKE: Students often forget to consider the negative sign of the energy, which indicates a decrease in the planet's mass.