What is the value of acceleration due to gravity, g, 400 km above Earth’s surface, where the International Space Station is in orbit? [G = 6.67 ×…
Source: JAMB · 2024
What is the value of acceleration due to gravity, g, 400 km above Earth’s surface, where the International Space Station is in orbit? [G = 6.67 × 10⁻¹¹ Nm²kg⁻², mass of Earth, M_E = 5.96 × 10²⁴ kg, radius of Earth, R_E = 6.37 × 10⁶ m]
Explanation
Use g = GM/r². The distance r is measured from Earth’s centre: r = 6.37 × 10⁶ + 4.0 × 10⁵ = 6.77 × 10⁶ m.
GM = 6.67 × 10⁻¹¹ × 5.96 × 10²⁴ = 3.975 × 10¹⁴. r² = 4.583 × 10¹³. So g = 3.975 × 10¹⁴ ÷ 4.583 × 10¹³ ≈ 8.67 ms⁻². It is only a little less than 9.8 ms⁻² on the ground.
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