# At 353.34 km, what percent of their surface-of-the-Earth weight will an astronaut have? In other words, if?

their weight is 100% when they are on Earth, what percent of that value is their weight when they are in orbit at the elevation of 353.34 km. Remember that altitude is the distance above the Earth's surface, not the distance from the center of the Earth. Altitude based on International Space Station (ISS).

Relevance

Mean Earth radius (from wikipedia) = 6371km

(6371 km + 353km) / 6371 km = 1.055

The astronaut's radius in orbit is 1.055 times as great as when he is on the ground.

Weight is inversely proportional to the square of the radius.

1 / (1.055)^2 = 0.8985

He will weigh about 90% of his weight on Earth.

This is all using the gravitational definition of weight (see source).

• Someone else got it, ~94% is right. The reason they float around is because they're in orbit.

You know how something follows a curve path when thrown, launched, shot, whatever? Well the same is true for anything in orbit. Now compare the curve of something you gently toss, to the curve of a baseball hit by a baseball bat. Now think of the ballistic path artillary makes. Now ballistic missiles... Getting there... and Now, the Space Shuttle. The Space Shuttle is going so fast it's curve is the same as the curve of the Earth.

Or think of it another way: It's going so fast, by the time it reaches the ground, it's already far enough away, that, because of the curve of the Earth, it hasn't hit the ground.

Or think of it this last way: The centrifugal force (you know, spinning bucket of water.) is equal to gravity, so the two cancel out.

• Answer: The astronaut's weight is zero.

If he/she happened to hop on some scales, it would register 0.0 kg = 0.0 lb.

An object in orbit around the earth is in free fall. That is to say it is falling toward the centre of the earth because it is attracted by Earth's gravity.

The astronaut still has mass. If he/she wanted to move to a different position inside the ISS a force proportional to the mass would need to be applied. And it would to be applied in the opposite direction to cease the movement.

• by moving a million radius removed from the exterior of the earth, you're doubling the term r interior the gravitation stress equation. simply by fact r is squared, you may divide by r² = 2² = 4. consequently a 800 N guy on the exterior of the earth could have a weight of 800/4 whilst a million earth radius intense. His weight would be 200N