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2 months ago

8

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?

1 answer:

Maru [3.3K]2 months ago

6 0

Answer:

85.31 N

Explanation:

The following information is given:

Earth's Radius = 3960 miles = 6373 Km

Astronaut's weight at sea level = 200lb = 90.72 Kg

Astronaut's altitude above the Earth = 125 miles = 201.17 km

We utilize the formula:

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

where,

F represents the gravitational force on the object, also known as weight

m is the object's mass = 200 lb = 90.71 kg

g represents the gravitational acceleration = 9.8 m/s²

Also,

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

where,

F stands for the gravitational force

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

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

r indicates the separation distance of the two objects

where r = (6373+201.17)km = 6574170 m

Using equation (1),

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

Substituting the value of m into equation (2)

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

$F=85.31N$

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