An astronaut who normally weighs 160 pounds at the Earth's surface travels away from the Earth. What would the astronaut weigh at the following distances from the surface of the Earth? Consider the Earth's radius to be approximately 4000 miles.

a. 4000 miles:

b. 8000 miles:

c. 12,000 miles:

d. 16,000 miles:

e. 20,000 miles:

An astronaut's weight decreases as they travel away from Earth because gravitational force decreases with the square of the distance from the Earth's center. At one Earth radius away, the weight is one quarter of the Earth weight, and it continues to decrease at greater distances following an inverse square law.

Explanation:

An astronaut's weight is the force due to gravity that acts upon their mass. Weight is calculated using Newton's law of universal gravitation, which states that the weight (force) is the product of the mass of the astronaut and the acceleration due to gravity (F = m*g). As an astronaut moves away from the Earth, the force of gravity decreases because the acceleration due to gravity is inversely proportional to the square of the distance from the center of the Earth. Therefore, at each of the given distances, the astronaut's weight would be:

a) At 4000 miles from the surface (or one Earth radius away), the weight would be one quarter of the weight on Earth.
b) At 8000 miles (two Earth radii away), the weight would be one ninth of the weight on Earth.
c) At 12,000 miles (three Earth radii away), the weight would be one sixteenth of the weight on Earth.
d) At 16,000 miles (four Earth radii away), the weight would be one twenty-fifth of the weight on Earth.
e) At 20,000 miles (five Earth radii away), the weight would be one thirty-sixth of the weight on Earth.

These ratios arise from the square of the distance increasing, which causes the force to decrease since gravitational force is inversely proportional to the square of the distance (F ≈ 1/d²).