You have probably seen films of astronauts floating weightless in orbiting satellites. People often get the idea that the astronauts are weightless because they are so far from the gravity of the earth. Let us see if that explanation is correct.

Question

You have probably seen films of astronauts floating weightless in orbiting satellites. People often get the idea that the astronauts are weightless because they are so far from the gravity of the earth. Let us see if that explanation is correct.

Typically, such satellites orbit around 400 above the surface of the earth. If an astronaut weighs 630 on the ground, what will he weigh if he is 400 above the surface?

In light of your answer to part A, are the astronauts weightless because gravity is so weak? Why are they weightless?

Answer 1

To find out what an astronaut would weigh 400 km above the surface of the Earth, we need to understand how gravity decreases with distance from the Earth's surface. The force of gravity can be calculated using Newton's law of universal gravitation, which states that the force between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them.

Let's assume that the mass of the Earth remains constant and the radius of the Earth is approximately 6,371 km. When the astronaut is on the Earth's surface, their weight is a measure of the force of gravity acting on their body. So, if they weigh 630 pounds on the ground, we can say that gravity is exerting a force of 630 pounds on their body.

When the astronaut is 400 km above the surface, the distance between the astronaut and the center of the Earth has increased by 400 km. Using the inverse square law, we can determine the ratio of the forces of gravity at these two distances:

(Radius of Earth / (Radius of Earth + Altitude))^2

Substituting the values, the ratio of the forces of gravity at the two distances would be:

(6371 / (6371 + 400))^2

Now, to find the weight of the astronaut 400 km above the surface, we multiply this ratio by their weight on the ground:

Weight 400 km above = (6371 / (6371 + 400))^2 * 630

By performing the calculations, we find that the weight of the astronaut 400 km above the surface would be approximately 567 pounds.

Now, let's address the second part of your question. Astronauts are not weightless because gravity is weak in space. In fact, gravity does exist in space, including in the orbiting satellites. The reason why astronauts appear weightless in orbit is due to the concept of freefall.

In orbit, satellites, including the International Space Station (ISS), are continuously falling towards the Earth but are also moving forward fast enough to keep missing it. This continuous falling motion creates a feeling of weightlessness for astronauts inside the spacecraft.

Since both the astronaut and the spacecraft are falling together, there is no solid surface resisting their motion. Therefore, astronauts experience the sensation of weightlessness because they are in a state of freefall.

To summarize, if an astronaut weighs 630 pounds on the ground, they would weigh approximately 567 pounds when they are 400 km above the Earth's surface. The weightlessness experienced by astronauts in orbit is not due to the weakness of gravity, but rather the continuous state of freefall they are in as they orbit the Earth.