Energy of orbiting satellites

Universal gravitation · Physics

Solar system

Interactive 3D

All eight planets in orbit around the Sun, with Saturn's rings and Earth's Moon.

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Study notes

A 500-kg satellite moves in a circular orbit of radius 8.0 × 10⁶ m around Earth. Find its KE, PE and total energy. (GM = 3.98 × 10¹⁴ m³/s²) Step 1: KE = GMm/(2r) = (3.98 × 10¹⁴ × 500) / (2 × 8.0 × 10⁶) = 1.99 × 10¹⁷ / 1.6 × 10⁷ = 1.24 × 10¹⁰ J. Step 2: PE = −GMm/r = −2 × KE = −2.49 × 10¹⁰ J. Step 3: E = KE + PE = 1.24 × 10¹⁰ − 2.49 × 10¹⁰ = −1.24 × 10¹⁰ J = −KE. Answer: KE ≈ +1.24 × 10¹⁰ J, PE ≈ −2.49 × 10¹⁰ J, E ≈ −1.24 × 10¹⁰ J. The negative total confirms the satellite is bound to Earth.