What Distance from Earth Achieves Weightlessness for Astronauts?

[bcjochim07]

Homework Statement

How far away from Earth does a spacecraft have to be for the astonauts in it to be weightless?

Homework Equations

The Attempt at a Solution

Is this correct:

Since the gravitational force is a long range force, no matter what finite distance the spacecraft and Earth are from each other, there will still be gravitational attraction. In order for the astronauts to be truly weightless the distance between the ship and the Earth would have to be infinite.

-I had second thoughts about what weightless meant. My book define weight as a normal force, so if the astronauts are floating around in the spacecraft , they have no normal force acting on them, but are they truly weightless?

 

[Dick]

You are correct. There is still a gravitational force whatever the distance. But if the vehicle you are traveling in is accelerating at the same rate you are due to that force, then that force produces no normal force. You have to choose one definition or the other. They don't agree. Most people would call astronauts 'weightless', even though in low Earth orbit the g force on them is not that much less than the ground.

 

[Moetasim]

Your answer is mostly correct, but there are a few things to clarify.

Firstly, weightlessness refers to the sensation of not feeling any gravitational force on your body. It does not necessarily mean that there is no gravitational force acting on you. So, in this case, weightlessness would occur when the astronauts are far enough away from Earth that they do not feel any gravitational force on their bodies.

Secondly, it is not necessary for the distance between the spacecraft and Earth to be infinite for the astronauts to be weightless. In fact, there is a specific distance at which the gravitational force between the two objects becomes negligible and the astronauts would feel weightless. This distance is known as the point of zero gravity or the Lagrange point, and it is approximately 1.5 million kilometers away from Earth.

Lastly, it is important to note that even at this distance, there is still a gravitational force acting on the astronauts and the spacecraft. However, the force is so small that it is practically negligible and can be considered as weightless.

In summary, weightlessness occurs when the astronauts are far enough away from Earth that they do not feel any gravitational force on their bodies, typically at a distance of 1.5 million kilometers. However, there is still a gravitational force acting on them, but it is so small that it can be considered negligible.