Physics

Physics

Problem

Calculate the magnitude of the gravitational force exerted by Earth (mass 5.97×1024 kg5.97\times10^{24}\,\text{kg}) on a 1.20×103 kg1.20\times10^{3}\,\text{kg} satellite that is 7.00×106 m7.00\times10^{6}\,\text{m} from Earth’s center. Give your answer in scientific notation with appropriate units.
Intuitive explanation

Gravitational force is fundamentally about how mass curves spacetime, but Newton's law of universal gravitation gives us a practical formula: F=Gm1m2r2F = G\frac{m_1 m_2}{r^2}. The key insight is that this force depends on both masses and drops off sharply with distance—notice the inverse-square relationship. You just need to plug in the numbers carefully, keeping track of powers of 10, and let the math reveal how strongly Earth pulls on the satellite.

Intuitive explanation

Gravitational force is fundamentally about how mass curves spacetime, but Newton's law of universal gravitation gives us a practical formula: F=Gm1m2r2F = G\frac{m_1 m_2}{r^2}. The key insight is that this force depends on both masses and drops off sharply with distance—notice the inverse-square relationship. You just need to plug in the numbers carefully, keeping track of powers of 10, and let the math reveal how strongly Earth pulls on the satellite.

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