Gravitational time dilation…science!

· 1 month ago

Marc just did a video on this-

https://youtu.be/jyIo0e4tSOc?si=o0x93DzIeQ8QL9VC

Dallen

· 1 month ago

Fun related fact: The distance from the center of Earth's gravity well, its center of mass, is greater as you move toward the equator, since the Earth widens a bit due to the centrifugal aspect of its rotation and the equator being the furthest, fastest latitude from the axis of rotation. You could think of it like spinning a squishy ball so fast that it turns into a disc shape, but the effect on Earth is much less dramatic. This does affect the passage of time in the same way that going up in a building does, as the article mentions. People far from the equator have their time slowed more significantly by the Earth's gravity well than people near the equator, by virtue of being deeper in the gravity well.

However, the people on the equator are also traveling a greater distance as the Earth rotates, since they are on a larger circumference path around Earth's axis, so they are moving at a greater velocity. Velocity also has relativistic time dilation effects. The people near the equator are further from the gravity well and experience less slowing of time from it, but they experience more slowing of time from their greater relative velocity.

It just so happens that, as you go up and down through the latitudes on Earth's surface, the time dilation effects of smaller latitudes being both further from the gravity well and traveling at greater relative velocities cancels out virtually entirely and coincidentally. It's not something that really cancels out in the math as a rule. It just so happens to for Earth at its size, density, and rotational velocity.

As a less related but still fun fact: Satellites zipping around Earth are traveling very quickly relative to us, which slows their time down, but they're also significantly further from Earth's center of gravity. Despite traveling so fast, they actually experience time more quickly than us and have to be adjusted to count time too slowly, because the time they would lose from traveling so fast is made up for and then some by the time they gain from being further from Earth.

I'm recounting this from learning about it a while ago, so if anyone remembers better or looks it up, feel free to correct me if I wrote anything that's wrong. I did use some less precise language to make it a bit simpler to read, but I don't think any of it was so loose as to be outright misleading.

Dallen

· 1 month ago

Dallen

Fun related fact: The distance from the center of Earth's gravity well, its center of mass, is greater as you move toward the equator, since the Earth widens a bit due to the centrifugal aspect of its rotation and the equator being the furthest, fastest latitude from the axis of rotation. You could think of it like spinning a squishy ball so fast that it turns into a disc shape, but the effect on Earth is much less dramatic. This does affect the passage of time in the same way that going up in a building does, as the article mentions. People far from the equator have their time slowed more significantly by the Earth's gravity well than people near the equator, by virtue of being deeper in the gravity well.

However, the people on the equator are also traveling a greater distance as the Earth rotates, since they are on a larger circumference path around Earth's axis, so they are moving at a greater velocity. Velocity also has relativistic time dilation effects. The people near the equator are further from the gravity well and experience less slowing of time from it, but they experience more slowing of time from their greater relative velocity.

It just so happens that, as you go up and down through the latitudes on Earth's surface, the time dilation effects of smaller latitudes being both further from the gravity well and traveling at greater relative velocities cancels out virtually entirely and coincidentally. It's not something that really cancels out in the math as a rule. It just so happens to for Earth at its size, density, and rotational velocity.

As a less related but still fun fact: Satellites zipping around Earth are traveling very quickly relative to us, which slows their time down, but they're also significantly further from Earth's center of gravity. Despite traveling so fast, they actually experience time more quickly than us and have to be adjusted to count time too slowly, because the time they would lose from traveling so fast is made up for and then some by the time they gain from being further from Earth.

I'm recounting this from learning about it a while ago, so if anyone remembers better or looks it up, feel free to correct me if I wrote anything that's wrong. I did use some less precise language to make it a bit simpler to read, but I don't think any of it was so loose as to be outright misleading.

I looked it up, and it seems Low Earth Orbit (less than 2,000km from the surface) is actually close enough to earth and fast enough that the difference in velocity relative to us has a more significant effect on time than the difference in distance to Earth's center of gravity. We don't put much in LEO, but the ISS is there for ease of access from the ground. What I said about satellites in general, that their clocks would be too fast, doesn't apply to really low altitude satellites. For LEO, the clocks are too slow, and there should be an orbit where the time dilation effects cancel out around 10,000km from the center of the Earth according to this graph.

aliveandticking

· 1 month ago

Dallen

I looked it up, and it seems Low Earth Orbit (less than 2,000km from the surface) is actually close enough to earth and fast enough that the difference in velocity relative to us has a more significant effect on time than the difference in distance to Earth's center of gravity. We don't put much in LEO, but the ISS is there for ease of access from the ground. What I said about satellites in general, that their clocks would be too fast, doesn't apply to really low altitude satellites. For LEO, the clocks are too slow, and there should be an orbit where the time dilation effects cancel out around 10,000km from the center of the Earth according to this graph.