/sci/ - Science & Math

[Anonymous No.4106569]

/sci/ there is a question that I'm dying to know the answer to and I was hoping you could help me out.

Does shape influence gravity? From the perspective of a subject within the shape's gravitational field I mean, not like... total gravity. Is that a thing? Anyway...

Assuming a homogenous density with unchanging mass and volume, how would the gravity on an Earth sized sphere of mass change in relation to somebody standing on various points of its surface if it was deformed into the shape of a disc? A cube? A long cylinder?

Like, if a person stood on the rim of the disc shaped Earth, would they experience any change in gravitational force compared to if they were standing on the flat surface of the disc? Would they feel more gravity or less?

My automatic assumption was that they would feel more gravity on the rim of the disc but I became muddled while trying to reason it out. I mean, yeah there's a greater concentration of mass directly below their feet but a lot of it is very far away. I'm confusing myself now, please help.

Disregard how they would feel due to air pressure.

Also, there are no elephants and no turtle holding up the discworld. Heh.

[Anonymous No.4106586]

You can treat any object as if all the gravity were coming from a point at the center of its mass. Shape doesn't matter; unless you're actually inside of the object.

[psistar !!bRma1Ao62vX No.4106590]

>>4106586
This.
But if it's disc-shaped, you could get very close or very far from the center, and experience huge changes. That could be funny, actually.

[Anonymous No.4106627]

So... wait what? Shape doesn't matter unless you're inside it or shape does matter when you're changing how far you are from the center?

[Anonymous No.4106657]

so... suppose gravity at the density center of a planet...

[Anonymous No.4106662]

>>4106627

The shape determines the center of mass, assuming the object is of uniform density. Once the center of mass is determined, you can think of gravity as concentrated at the center of mass.

[Anonymous No.4106672]

>>4106627
If you were standing on a disk-world the force of gravity would be pulling you towards the disk's center of mass, which isn't going to be directly below you. You'll be pulled sideways and down until you're standing on top of the center of the disk; at which point gravity will be pulling you straight down with a great deal of force.

[Anonymous No.4106682]

>>4106672
I see. But if you were braced perfectly on the edge of the disc, like, the outside edge of the ring, would the gravity you feel be "higher" than the gravity you would feel standing right over the middle of the flat face?

[Anonymous No.4106709]

>>4106682
On the edge of a disk you would be much further from the center of gravity so the force of gravity would be much less. The force of gravity between two objects is proportional to the inverse square of the distance between their centers of mass.

[Anonymous No.4106731]

>>4106709
>>4106682

So no, you'd weigh less at the edge. You weigh less in Denver then you do in Holland. That is why everyone in Holland is fat.

[Anonymous No.4106745]

Shape greatly affects gravity. The well-known map of the ocean floor from the 70s relies on this fact.

Satellites flew over the oceans using radar to measure the height of the surface. Since the Earth is not actually a sphere, the water in the ocean collected over underwater mountains raising the surface level a little bit.

Calibrating the data with known depth data, they were able to create a highly detailed map of the world's ocean floor. In this survey, they even discovered several features that had not been suspected.