If an astronaut weighs 750 N on the ground, what will he weigh in earth orbit 400 km above the earth’s surface? R_earth = 6.38 × 10^6 m,
m_earth=5.97×10^24 kg
G=6.674×10^−11 Nm^2/kg^2

The weight of the astronaut in Earth's orbit 400 km above the Earth's surface is 664.115 N

Explanation:

The given parameters are;

The weight of the astronaut on the ground = 750 N

The height of the orbit above the Earths surface = 400 km

The radius of the Earth = 6.38 × 10⁶ m

The mass of the Earth = 5.97 × 10²⁴ kg

The universal gravitational constant G = 6.674 × 10⁻¹¹ Nm²/kg²

From Newton's law of universal gravitation, we have;

= ((6.38 × 10⁶)² × 750)/((6.674 × 10⁻¹¹) × (5.97 × 10²⁴)) ≈ 76.62 kg

The mass of the astronaut ≈ 76.62 kg

For the weight of the astronaut  in Earth orbit 400 km (400 × 10³ m) above the Earth's surface, we have;

The weight of the astronaut in Earth's orbit 400 km above the Earth's surface = 664.115 N.

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