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Gravitational potential due to standard bodies

Universal gravitation · Physics

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Let's find the gravitational potential (V) at the surface of the Earth. Step 1: Identify the values. Mass of Earth (M) = 6 × 10^24 kg. Radius of Earth (r) = 6.4 × 10^6 meters. Gravitational constant (G) = 6.67 × 10^-11 Nm²/kg². Step 2: Use the formula V = -GM / r. Step 3: Put the numbers in. V = -(6.67 × 10^-11) × (6 × 10^24) / (6.4 × 10^6). Step 4: Multiply the top numbers: 6.67 × 6 = 40.02. Combine powers of 10: 10^-11 × 10^24 = 10^13. So, 40.02 × 10^13 / 6.4 × 10^6. Step 5: Divide 40.02 by 6.4 = 6.25. Step 6: Solve powers of 10: 10^13 / 10^6 = 10^7. The result is -6.25 × 10^7 Joules per kilogram.

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