Question

An astronaut weighs 200 lb at sea level. The radius of the earth is 3960 miles. What force is exerted on the astronaut if he is floating 125 miles above the earth's surface?

Answer 1

Answer:

85.31 N

Explanation:

Given,

Radius of Earth = 3960 miles = 6373 Km

Weight of Astronaut at Sea level = 200lb = 90.72 Kg

Altitude of Astronaut above Earth = 125 miles = 201.17 km

We know that,

$F = m\times g$ --------------------------  (1)

where,

F = force on the object due to gravity also called the weight

m = mass of the object = 200 lb = 90.71 kg

g = acceleration due to gravity = 9.8 m/s²

Also,

$F = \frac{GMm}{r^{2}}$ -------------------(2)

where,

F = force due to gravity

G = Gravitational constant = $6.67\times 10^{-11}$ Nm²/kg²

M = mass of the Earth = $5.97\times 10^{24} kg$

r = distance between the two objects

here, r = (6373+201.17)km = 6574170 m

From equation (1),

$m\times g = 90.71\\m=\frac{90.71}{g} \\m=\frac{90.71}{9.8}\\m=9.26 kg$

Putting value of m in equation (2)

$F = \frac{6.67\times 10^{-11}\times 5.97\times 10^{24}\times 9.26}{6574170^{2}}$

$F=85.31N$