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
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.
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.
It would be downhill. Since the direction you walk is tangent to the force of gravity, you would always be stepping forward and down a little, no matter what direction go.
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.
Gravity always pulls you towards the centre of the Earth. This means that when you’re standing on the North pole you’re being pulled in a totally different direction than someone standing on the equator.
If you were to walk around the entire Earth from pole to pole you wouldn’t walk uphill then downhill, you’d walk along a constant curve but the angle you were being pulled at would constantly change to always pull you “down” so the ground would always seem flat to you. (Obviously this wouldn’t hold true for actual hills & mountains, which you would have to climb and descend, and there would be a lot of ocean for you to “walk” on, but for this example I’m assuming you’re walking exclusively at sea level)
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.
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