A 1000-kg satellite orbits Earth at a height of 1000 km above the surface. Find its binding energy. (R = 6.37 × 10⁶ m, g = 9.8 m/s²) Step 1: Orbital radius r = R + h = 6.37 × 10⁶ + 1.0 × 10⁶ = 7.37 × 10⁶ m. Step 2: Binding energy = GMm/(2r). Use GM = gR² = 9.8 × (6.37 × 10⁶)² = 3.976 × 10¹⁴ m³/s². Step 3: BE = (3.976 × 10¹⁴ × 1000) / (2 × 7.37 × 10⁶) = 3.976 × 10¹⁷ / 1.474 × 10⁷ ≈ 2.70 × 10¹⁰ J. Answer: ≈ 2.7 × 10¹⁰ J (27 GJ). That is the energy of about 6.5 tonnes of TNT — freeing a satellite takes an enormous punch, which is why dead satellites stay up there.