How can you accurately measure your weight on Jupiter without a solid surface?

[Math Is Hard]

This was a bonus question on my astronomy homework, but my knowledge of basic physics is so incredibly limited that I am really struggling with it. It's bugging me because I'd just really like to know how this works.

"Given that Jupiter has no solid surface, how could you weigh yourself on Jupiter?"

Well, first I calculated acceleration of gravity on Jupiter and I got about 25 meters per second squared.

Then, I thought about riding in an elevator on Earth and I know that if you are accelerating downward, your weight is decreasing. If you are plummeting at 9.8 m/s^2 (Earth's acceleration of gravity) then you should feel no weight all. (I think ..?)
If the elevator starts accelerating back up very fast, your weight is going to increase.

My feeling is that you would need to be accelerating upward (in a special space-craft, maybe)at a certain rate to take a measure of your weight on Jupiter. But I am kinda lost now.

Thanks in advance for your help :)

 

[Ambitwistor]

If you're not on a solid surface, you are presumably floating around in Jupiter's atmosphere somewhere. Can you think of a way to stand on a scale while floating around in the air?

 

[HallsofIvy]

My feeling is that you would need to be accelerating upward (in a special space-craft, maybe)at a certain rate to take a measure of your weight on Jupiter. But I am kinda lost now.

Actually, that's a good start! And, after a few minutes of pondering it, I think I understand ambitwistor's suggestion too!

Of course, you would want your "scale", sitting in your "special space-craft" to be motionless itself with respect to Jupiter. Perhaps you could use radar to determine you distance with respect to whatever surface there is (there is, I believe something like a liquid surface, or perhaps just an isocline would do).

In order to be motionless relative to Jupiter, what does your space-craft have to be doing? If you now stand on a scale, what does that scale tell you?

 

[Math Is Hard]

Hello HallsOfIvy and Ambitwistor,

Hmmm... do I need to keep my spaceship at a fixed altitude over the "surface"? Would that do it? In which case I would have to be accelerating enough to fight gravity and hold my altitude steady. Would an upward acceleration of 25 m/s^2 be enough to hold me in place at that altitude? (and can you call it acceleration if you're staying in one place?)
Ambitwistor, were you suggesting that maybe I could hang from a scale instead of standing? (I probably completely misinterpreted that, but I thought I'd give it a shot.)
Thank you both!

 

[Ambitwistor]

Originally posted by Math Is Hard
Hmmm... do I need to keep my spaceship at a fixed altitude over the "surface"?

Yes.

In which case I would have to be accelerating enough to fight gravity and hold my altitude steady. Would an upward acceleration of 25 m/s^2 be enough to hold me in place at that altitude?

You need to pick the altitude, such as the nominal radius of Jupiter, and calculate the gravitational acceleration at that altitude.

Of course, if you did that, you could just calculate your weight, too. In practice, you'd have to adjust your hovering to be relatively motionless with respect to the atmosphere -- you can do that by measuring airspeed velocity or something, without calculating -- and then step on a scale.

(and can you call it acceleration if you're staying in one place?)

It's not acceleration relative to the planet, but it is proper acceleration (it will show up on a scale).

Ambitwistor, were you suggesting that maybe I could hang from a scale instead of standing?

Not quite, but that could work, if you did it right.