My family members say you’re walking downhill from the north pole to the equator, and uphill going the opposite way, but that doesn’t make sense, because you’re still walking along an arc on the sphere. I’ve stared and stared and stared at this baseball in my hand, but can’t figure it out.
In: Physics
The earth is not a perfect sphere. The centripetal force makes the equator farther away from the core than the poles. Therefore as you walk toward the equator you are going up, and as you go toward the poles you go down.
The idea of North being above South was actually decided by chance. South could also be considered the “top” of the Earth, because it’s arbitrary. The Earth doesn’t really have a top or a bottom.
We define “up” and “down” relative to the direction of gravity, and gravity always pulls towards the center of the Earth. So whether you’re in Antarctica or Brazil, “up” is away from the center from the Earth, and “down” is towards the center.
Think about a golf ball. If you were microscopic and walking around on that golf ball like it were a planet you’d go uphill and downhill over and over walking in any direction. But why? At any point, draw a line from you to the exact center of that golf ball. Unless that line intersects the surface of that golf ball at 90 degrees, you aren’t on flat ground. The only “level” ground on the golf ball would be at the bottom of each dimple, or on the tops of the ridges in between them. The golf ball has no “north pole” or equator. The direction you walk along the golf ball doesn’t generalize to “always uphill” or “always downhill ” in a certain direction.
It’s not hard if you first actually define what “up” and “down” mean. Down means toward the center of gravity, or the middle of the earth in this case, and up means away from it. Assuming a perfectly smooth, round surface like a ball (which the actually Earth isn’t. It’s rather lumpy and mishappen) you would not going uphill or downhill since you won’t be getting any closer to the center of the Earth or farther away.
If it helps, I will add that the reason going up a hill take extra work is that we are literally fighting against gravity, pushing to get away from the middle of the earth. The steep the hill, the faster we are trying to move away and the hard it is. Going downhill, however, gravity is pulling is down which is why is is so easy. Gravity is trying to pull us closer to the center of the Earth anyway, so we dont’ have to work at is so hard ourselves.
But as I said, you are doing neither in your scenario.
On a perfect sphere, your center of mass isn’t moving up or down no matter how far you walk. “Downhill” doesn’t exist from your point of view, essentially.
Walking from pole to equator, you’re walking uphill because the Earth is spheroid, fatter at equator than pole. So your distance from center of Earth would be larger at sea level at equator than sea level at pole.
If the world was a perfect sphere, I believe you would essentially be walking on a flat surface. As you take a step, the “top” of the sphere would be right in the middle of your feet. As your step gets larger, your landing foot would keep getting further “below” the “top”. However, as the “top” is right between your feet, your stationary for is also “dropping” further ” below” the “top”, making your feet at the same height once your foot lands.
If Earth were a perfect sphere, you would never walk uphill or downhill. That perception is entirely based on being internally level, so if you were to walk along a perfect sphere the size of Earth, you would always remain level because the direction in which gravity pulls you is constantly changing. In other words, your distance from the sphere’s center would never change.
Constantly downhill. Think of a large ball and put your finger on the very top. No matter which direction you love your finger, it will have to go down to remain on the surface of the ball.
That’s assuming a perfect sphere with no imperfections. On earth, obviously the ground is oddly shaped: mountains, valleys, etc make you have to literally up and downhill.
When an object is in orbit it is said to be falling, it just has enough forward momentum to never hit the ground. Using this as a basis, I would say you are constantly walking downhill.
Now of course, the earth isn’t a perfect sphere so you are going up and down. If it was a perfect sphere, downhill is the way to go.
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