How Does Apparent Weight Change for an Astronaut Near the Moon?

[Abu]

Homework Statement

What is the apparent weight of a 70-kg astronaut 3800 km from the center of the Earth's Moon in a space vehicle when
a) Moving at a constant velocity
b) Accelerating toward the Moon at 2.9 m/s^2?

State direction in each case

Homework Equations

wt = m(g+a)
wt = m(g-a)
Fgr = GmM/r^2

The Attempt at a Solution

So for a) I first found the acceleration due to gravity at that point, which is
g = GM/r^2
The mass of the moon is 7.36x10^22
g = 6.67x10^-11 (7.36x10^22)/3800000
g = 0.33 m/s

At a constant velocity, the weight is simply mg. So, 70x0.33 = 23.7 Newtons

For b however, I am not entirely sure. This is what I was thinking when I was trying to solve the problem:
Since you are accelerating at 2.9m/s^2 towards the moon, I will use wt = m(g-a) because I was taught that when going against the force of gravity, the wt = m(g+a) is used, and vice versa.
I get the following answer:
wt = 70(0.33 - 2.9)
= -179.9 Newtons

Now I have a couple of problems. I am not sure what direction these values for a) and b) are pointed towards and if a negative apparent weight is even possible (or if that answer is even correct in the first place).

Thank you very much for your patience.

 

[haruspex]

am not sure what direction these values for a) and b) are pointed towards and if a negative apparent weight is even possible (or if that answer is even correct in the first place).

Your work looks correct to me.

 

[Abu]

Your work looks correct to me.

Thank you very much for your response.

I am glad my work checks out, though I can't seem to wrap my head around why the answer for part b is negative..

Included in that is my confusion regarding which direction these apparent weight forces should be pointing:

My first guess is that for a) there really is no apparent weight because the object is moving at a constant velocity, hence the answer I think would be its gravitational force of attraction directed towards the moon.

I am not sure about b) though..

Thank you for your time.

 

[haruspex]

why the answer for part b is negative..

Because weight is, by definition, a force due to gravity, so apparent weight would be the apparent force in the direction of the gravitational field. If the astronaut feels as though a mysterious is pushing her away from the moon then the apparent weight is negative.

 

[Abu]

Because weight is, by definition, a force due to gravity, so apparent weight would be the apparent force in the direction of the gravitational field. If the astronaut feels as though a mysterious is pushing her away from the moon then the apparent weight is negative.

Thank you for your time, and sorry for the late response - I got caught up in some other subjects...

So is this what occurs when one were to accelerate at a rate greater than the gravity acting on them? It would feel as though they were getting pushed away? If so... why does this happen? I am assuming that this would also apply to if you were somehow accelerating downwards faster than 9.81 m/s^2 while in an elevator, and thus you would be pushed by some force towards the ceiling of the elevator?

Once again, thank you for your responses.

 

[haruspex]

It would feel as though they were getting pushed away?

Yes. Gravity would not be enough to make them accelerate at that rate, so an additional force must be pushing them towards the planet. The astronaut would feel that force as an externally applied force. In the astronaut's frame of reference there is no acceleration. To explain that, despite the felt force, it would feel as though some other pervading force, like gravity, were pushing them up against it.
This is just like the everyday experience of gravity, but inverted. You feel the force of the floor on you, but you are not accelerating, so infer the force of gravity pushing you against the floor.

this would also apply to if you were somehow accelerating downwards faster than 9.81 m/s^2 while in an elevator, and thus you would be pushed by some force towards the ceiling of the elevator?

Yes. Indeed, you would not exceed 9.81 m/s^2 until you found yourself pressed against the ceiling.