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

In summary: At that point you might be able to push off the ceiling to increase your acceleration further, but that would be difficult.In summary, the apparent weight of a 70-kg astronaut 3800 km from the center of the Earth's Moon in a space vehicle is 23.7 Newtons when moving at a constant velocity and -179.9 Newtons when accelerating towards the Moon at 2.9 m/s^2. This negative apparent weight occurs because the astronaut is accelerating at a greater rate than the gravitational force acting on them, causing them to feel a force pushing them away from the Moon. This is similar to the everyday experience of gravity, but inverted.
  • #1
Abu
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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.
 
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  • #2
Abu said:
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.
 
  • #3
haruspex said:
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.
 
  • #4
Abu said:
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.
 
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  • #5
haruspex said:
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.
 
  • #6
Abu said:
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.
Abu said:
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.
 

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

1. What is the apparent weight problem?

The apparent weight problem is a phenomenon that occurs when an object is placed on a scale and its weight appears to be different than its actual weight. This can happen due to various factors such as the presence of an external force, acceleration, or gravitational pull.

2. How does acceleration affect apparent weight?

Acceleration can affect apparent weight by changing the normal force acting on an object. When an object is accelerating, the normal force may decrease, causing the apparent weight to also decrease. This is commonly observed in elevators, where a person may feel lighter or heavier depending on the direction of acceleration.

3. Why does the apparent weight of an object change on a scale in an elevator?

The apparent weight of an object changes on a scale in an elevator due to the acceleration of the elevator. When the elevator is accelerating upwards, the normal force acting on the object decreases, making it appear lighter. Conversely, when the elevator is accelerating downwards, the normal force increases, making the object appear heavier.

4. How does the presence of an external force affect apparent weight?

The presence of an external force can affect apparent weight by adding or subtracting from the normal force acting on the object. For example, if a person is standing on a scale and someone pushes down on their shoulders, the normal force acting on the person increases and their apparent weight will also increase.

5. How does gravity affect apparent weight?

Gravity can affect apparent weight by creating a normal force that is equal to the gravitational force acting on the object. When gravity is the only force acting on an object, the apparent weight will be equal to the actual weight. However, in situations where there are other forces involved, such as acceleration or external forces, the apparent weight may differ from the actual weight due to the changes in the normal force.

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