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April 18, 2012 7:22 AM

So, we live on a ball. When traveling in one direction, are you always going uphill? Or downhill?

Yes, yes, I know, we're technically on a sphere. And ignore that pesky elevation thing. Let's just say it's a flat, smooth ball/sphere. Are you always going uphill or downhill? Gravity, rotation, etc all are normal otherwise.

posted by rich to Science & Nature (27 answers total)

Are 'up' and 'down' not just relative to the direction of gravitational force on your body (i.e. towards the centre of your uniform sphere), or am I missing something in your question?
posted by pipeski at 7:25 AM on April 18, 2012 [2 favorites]

If it's a perfect sphere, then your distance from the center of the sphere will never change, so you are never going up or downhill, relative to the rest of the surface.
posted by Think_Long at 7:25 AM on April 18, 2012 [16 favorites]

Would you consider yourself to be walking "uphill" or "downhill" if you were walking across Kansas in one direction? I'm betting "no."

That's because concepts of "uphill" and "downhill" refer to protrusions from the sphere, not cardinal directions on the sphere itself. For the same reason, walking north or south across a flat plain doesn't feel like going "uphill" or "downhill" because gravity doesn't relate to cardinal direction.
posted by EmpressCallipygos at 7:26 AM on April 18, 2012 [1 favorite]

I take "down" to mean toward the direction of the mean gravitational pull, and "up" to mean away from that gravitational pull. On the surface of a sphere of uniform density, having minimal external gravitational influences, that direction should always be towards the center of the sphere. Any motion across the surface is motion neither towards nor away from the center of the sphere.

Therefore the answer is "neither."
posted by gauche at 7:26 AM on April 18, 2012

No. Uphill is moving away from the center of the sphere, and downhill moving towards the it. If the ball is completely flat, then your distance to the center never changes as long as you stay on the surface.
posted by qxntpqbbbqxl at 7:26 AM on April 18, 2012

You can't talk about uphill and downhill while ignoring elevation. It's like asking about whether someone's walking quickly or slowly while ignoring their speed.
posted by oliverburkeman at 7:28 AM on April 18, 2012 [2 favorites]

If you were always going downhill, then when you stood on your skateboard you would accelerate up to terminal velocity and keep going that speed for ever.

If you were always going uphill, you would be buried in a pile of people on skateboards.
posted by procrastination at 7:28 AM on April 18, 2012 [3 favorites]

On the one hand, neither. As the above answers say, if you stick perfectly to the surface then your distance from the center never changes.

On the other hand, downhill. Move tangentially to the surface, fall slightly, move tangentially, fall slightly, rinse, repeat. Move tangentially fast enough, and the sphere falls away at the same rate that you're falling towards it and presto, you're in orbit.

On the gripping hand, as the distance you move tangentially approaches 1/infinity, you are sticking perfectly to the surface, which sends us back to case one...
posted by penguinicity at 7:36 AM on April 18, 2012 [2 favorites]

I don't think you mean to say it's a FLAT, smooth ball/sphere, so I will assume you mean an earth-sized, perfectly sphere like planet we will call "New Earth". Our actual Earth is globoid, not spherical, or round.

Both Earth and "New Earth" have around a 15 mile eyesight before the curvature of the earth blocks our view, for flat areas. Earth has non-flat areas (mountains, canyons, etc.) while "New-Earth" has no non-flat areas. With objects this big as "New Earth", we should experience the sensation of walking a level ground any direction we go, since the sloping is so subtle that we will not experience it as a slope.

This, and we -- since we will always have the sense of being "on top" of the earth, regardless of our position on "New Earth" -- will perceive our current position and direction as being perfectly flat.
posted by spladoodlekeint at 7:38 AM on April 18, 2012

If you were always going downhill, you would not keep going forever, due to friction, contra a comment above. In any event, you walk along the surface of the Earth, which is neither a sphere nor a ball but rather an oblate spheroid. In any event, it doesn't make sense to refer to walking on the outer surface of a 3D object as going uphill or downhill.
posted by dfriedman at 7:39 AM on April 18, 2012

On the other hand, downhill. Move tangentially to the surface, fall slightly, move tangentially, fall slightly, rinse, repeat. Move tangentially fast enough, and the sphere falls away at the same rate that you're falling towards it and presto, you're in orbit.

Any move tangential to the surface of the sphere is not a move across the surface of the sphere (i.e., a change in elevation). This describes "jumping."
posted by gauche at 7:39 AM on April 18, 2012

we're technically on a sphere.

"Down" is towards the center of that sphere. "Up" is away from the center of that sphere. If you are walking on the surface of a smooth sphere, you remain the same distance from the center of that sphere, so are neither going up nor down.
posted by ook at 7:40 AM on April 18, 2012

Uphill and downhill are both directions within the frame of reference of sea level. Moving across the surface of the earth is not the same as moving up or down with reference to the distance between you and sea level. So it's neither.
posted by clockzero at 7:42 AM on April 18, 2012

The following is totally me just noodling around with the idea, but:

So taking this a step further: moving "uphill" or "downhill" means moving such that the component of your movement vector which is parallel to a line extending from the center of the earth through you is nonzero.

But there are other gravitational sources in the universe, notably the moon and the sun. Only in very special cases can you move such that you are moving "flat" relative to the center of the earth AND the moon AND the sun.

So you're almost always moving against SOME gravitational tug. When the tide comes in, I can conceptualize thinking of it as coming in because the earth has "tilted" relative to the sun, and therefore the water is pouring "downhill" ever so slightly.

Also, there are small and non-spheroidal objects in the solar system where you probably would be moving against gravity on a "flat" surface, although the gravity would be very very weak.
posted by endless_forms at 7:44 AM on April 18, 2012

Is the sphere spinning? Where are you on the sphere? Which direction are you walking? Do you want to consider up/down-hill in terms of potential+kinetic energy?
posted by zengargoyle at 7:45 AM on April 18, 2012

I thought when he said 'we live on a ball' he meant Earth. So, yeah it's spinning.
posted by spicynuts at 7:50 AM on April 18, 2012

Your trailing foot is planted on an uphill slope, your leading foot comes down onto a downhill slope. You are forever cresting an extremely gentle hill.
posted by contraption at 7:54 AM on April 18, 2012

So, we live on a ball. [...] Yes, yes, I know, we're technically on a sphere.

What do you imagine the distinction is?
posted by Rat Spatula at 8:19 AM on April 18, 2012

Response by poster: Yes, globoid is more accurate, which I imagine would mean that the distance to the center is not constant all the way around the spheroid object.. and on zengargoyle's point - more on the potential+kenetic energy/physics aspect rather than sensation.

when I originally was thinking about it, I ignored that the gravity would be coming from inside, rather than from some point outside of the sphere.

But contraption - couldn't you say your trailing foot is on a downhill slope and your leading foot is on an uphill slope?
posted by rich at 8:44 AM on April 18, 2012

Any move tangential to the surface of the sphere is not a move across the surface of the sphere (i.e., a change in elevation). This describes "jumping."

Then all movement along a sphere is jumping. If you're moving along a sphere, at any time your motion vector is straight along the tangent line. (It could be a higher angle if you're really jumping but there's no way you can go lower than the tangent -- not without bringing in picks and shovels anyway). In order to continue along the surface, some force has to accelerate you so that your motion vector is now along the new tangent. The slope of this new tangent is downhill compared to the previous one.
posted by penguinicity at 9:00 AM on April 18, 2012

If you were always going downhill, you would not keep going forever, due to friction, contra a comment above.

Hence the mention of terminal velocity in the comment. It could be that terminal velocity is zero, if the downhill slope is insufficient to overcome friction.
posted by procrastination at 9:01 AM on April 18, 2012

Perhaps it depends on your mood, in a glass-half-full/half-empty sort of way.

I always like going South; somehow, it feels like going downhill.
posted by Elly Vortex at 9:07 AM on April 18, 2012 [1 favorite]

Best answer: So, we live on a ball. [...] Yes, yes, I know, we're technically on a sphere.

What do you imagine the distinction is?

Specificity. Please don't be condescending when people ask science questions. It only discourages them from asking more questions. Which is the opposite of what I'm trying to accomplish in life.

Have you played Mario Galaxy? On some of the smaller worlds, you can run around the whole globe in a scenario that you describe. Up or down is just a frame of reference.

Now close your eyes and imagine that the earth is "upsidedown" and that gravity is pulling you and everything to the "ceiling". BRAIN MELT.
posted by JimmyJames at 9:09 AM on April 18, 2012 [2 favorites]

Best answer: On a perfect sphere of Earth's mass, the ground is rushing up at you at 9.8 m/s2. This is what keeps your feet on the surface—otherwise you'd float out into space. Therefore, you could, in a rhetorical sense, be said to be going 'downhill', to the extent that the ground is constantly coming up at you. This is not, however, an intuitive understanding of the term (or of the Newton's apple metaphor for how gravity is often portrayed to work in middle school).
posted by Blazecock Pileon at 9:16 AM on April 18, 2012 [1 favorite]

Best answer: This is why physics questions tend to be all like "consider a frictionless sphere of radius R with uniform density D and a point mass on the surface, Q: ...". The answer there is (IIRC) that the world is flat as far as the point mass is concerned. If the sphere didn't have uniform density, say it was denser towards the north, then a point placed not directly on but just beside the south pole would fall towards the north and being frictionless would end up in periodic motion accelerating around the north pole and up the other side to the south deaccelerating until it stopped the same distance from the south pole as it started (on the other side) and then start falling back to the north again.

If you're careful in your walking and use friction to push your center of mass while keeping it at the same distance from the center of the sphere then it's flat. If you walk like humans normally do what' you're doing is lifting one leg and falling forward, planting your foot and then lifting your center of gravity back up. (jumping is when both feet leave the ground :P)

It depends on where you start, you either go down then up (if you start with your legs together) or up then down (starting legs apart), if you shuffle about all kung-fu like then you glide across flat. One complete step leaves your center the same distance from the center of the sphere at the same potential energy level. You loose energy from friction with any atmosphere and the inefficiency of human muscles. In the perfect pointy physics it's a zero sum game, turning potential energy into kinetic and kinetic back into potential.

If you want to ponder globoids and rotation and friction etc. then things get more complicated. But you can take as a starting point that potential+kinetic is constant, moving with/against a gravitational field gives/takes energy, moving across a gravitational field doesn't. If you're not a point mass, don't forget the difference of the gravitational field between your feet and your head.
posted by zengargoyle at 10:20 AM on April 18, 2012 [1 favorite]

If you assume away all local elevation differences, and just treat the smooth spheroid, you could argue that you're never doing either - you're always cresting the hill. Your back foot and front foot are both downhill from your center of mass.

But maybe you could also make the argument that you're generally walking uphill if there's a southern component to your movement, as you move farther from the center of the Earth, and downhill for northern movement as you get closer. In the northern hemisphere, obviously. Then again, you could argue for southern movement being DOWNhill because you are moving toward a steeper local curvature, so your forward foot is traveling farther to maintain your equilibrium than when moving in the opposite direction.

In short, yes. No. Maybe. But probably not. Then again....
posted by solotoro at 10:45 AM on April 18, 2012

(And never mind that contraption beat me to the first bit.)
posted by solotoro at 10:48 AM on April 18, 2012