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Gravitational field and field intensity

Universal gravitation · Physics

Solar system

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

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Study notes

Calculate Earth's gravitational field intensity at a height of one Earth radius above the surface (i.e. at r = 2R_earth). (g at surface = 9.8 N/kg) Step 1: Field intensity follows E = GM / r², an inverse-square law. Step 2: At the surface, r = R and E = 9.8 N/kg. Step 3: At r = 2R, E = GM / (2R)² = (GM / R²) / 4 = 9.8 / 4 = 2.45 N/kg. Answer: 2.45 N/kg, directed toward Earth's centre. A 60-kg astronaut there would weigh only 60 × 2.45 = 147 N instead of 588 N — the field picture tells us the pull per kilogram directly.

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