Question

If John Glenn weighed 640 N on Earth's surface, a) how much would he haveweighed if his Mercury spacecraft had (hypothetically) remained at twice thedistance from the center of Earth? b) Why is it said that an astronaut is nevertruly "weightless?"

Answer 1

Given:

The weight of John Glenn, w=640 N

To find:

a) The weight if the distance was twice that of the initial value.

b) Why is an astronaut never weightless.

Step-by-step explanation:

a)

Let the distance between the spacecraft and the earth be r.

If it becomes twice, then the distance is 2r.

The initial gravitational force on John Glenn is,

`F=w=(GMm)/(r^2)`

Where G is the gravitational constant, M is the mass of the earth and m is the mass of John Glenn.

The force when the distance is twice,

`\begin{gathered} w_n=(GMm)/((2r)^2) \\ =(GMm)/(4r^2) \\ =(w)/(4) \end{gathered}`

On substituting the known values,

`\begin{gathered} w_n=(640)/(4) \\ =160\text{ N} \end{gathered}`

b)

Even when the astronaut is in space they still have the mass and so does the earth. Thus there will always be a gravitational force of attraction between the earth and the astronaut. The astronaut does not feel the weight because there will be nothing in space that pushes them back. That is why an astronaut is never truly weightless.

Final answer:

a) Thus the weight of John Glenn will be 160 N