Respuesta :
Answer:
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;
[tex]Weight \ on \ ground \ of \ astronaut \ F_W =G\times \dfrac{M_{Earth} \times m_{astronouat}}{R_{Earth}^{2}} = 750 \ N[/tex]
[tex]F_W =6.674 \times 10^{-11}\times \dfrac{5.97 \times 10^{24}\times m_{astronouat}}{(6.38 \times 10^6)^{2}} = 750 \ N[/tex]
[tex]m_{astronaut}[/tex] = ((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;
[tex]F_{W \ in \ orbit} =6.674 \times 10^{-11}\times \dfrac{5.97 \times 10^{24}\times 76.62}{(6.38 \times 10^6 + 400 \times 10^3)^{2} } = 664.115 \ N[/tex]
The weight of the astronaut in Earth's orbit 400 km above the Earth's surface = 664.115 N.
