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> We found that the moon was around 60,000 kilometers closer to the Earth then [2.46 billion years ago] (that distance is about 1.5 times the circumference of E

> We found that the moon was around 60,000 kilometers closer to the Earth then [2.46 billion years ago] (that distance is about 1.5 times the circumference of Earth). This would make the length of a day much shorter than it is now, at roughly 17 hours rather than the current 24 hours. I wish they explained why the moon being that much closer would have such a dramatic effect on the day length. Can someone explain this? Seems off to me, but I'm very physics-naive. Also, good to know it's drifting away, and not towards the earth!

mgraczyk 4y ago
To first order I think the explanation is just conversation of angular momentum. The moon earth system has to have it's angular momentum constant over time. If the moon is further away in a stable orbit, the earth must rotate slower.
morsch 4y ago
It's explained here: https://en.m.wikipedia.org/wiki/Tidal_acceleration https://en.m.wikipedia.org/wiki/Tidal_acceleration
FiatLuxDave 4y ago
Sure. The earth is spinning faster than the the moon is going around the earth (earth rotates in one day, the moon goes around in about a month). When the tides transfer energy and momentum to the moon from the earth's spin, it slows down the earth's spin and gives the moon more energy. This moves the moon to a higher orbit, so it moves a bit farther away from us. The source of energy for the whole process is the earth's spin. It takes a lot of energy to lift a moon, relative to the amount of energy in the earth's spin, which is why it has such a dramatic effect on the day length.
- redact207 4y ago
  If the moon wasn't drifting away and was in a static orbit, would the Earth's rotation slow and the moon's orbit speed up to the point where they're in sync?
  - yellowapple 4y ago
    Eventually, yeah; just as the Moon is tidally locked to Earth, Earth would be tidally locked to the Moon. I don't know offhand whether that would happen before the Moon drifts too far away to remain in Earth's orbit, however.
    - sliken 4y ago
      Moon is below escape velocity, so it's not leaving. In fact when 1 day = 1 lunar month the movement away will stop, and reverse. It will continue to get closer to earth until it hits the Roche limit and becomes a ring.
  - aussieshibe 4y ago
    Fair warning: everything I know about orbital mechanics is from Kerbal Space Program. The moon cannot orbit at a higher speed while keeping the same semi-major axis (average distance to the orbital centre of mass). If you suddenly doubled the orbital speed of the moon right now, the apoapsis (the highest point in its orbit relative to the orbital centre of mass) would increase significantly. If you slowly accelerate the moon in the direction of its orbital velocity consistently over a long time period, the moon will slow down relative to the Earth, but it's semi major axis will increase. Actual scientists of HN: have at me.
    - incompatible 4y ago
      Yeah, the moon isn't "drifting away" on its own, its being forced away as it takes energy from the Earth.
    - robertlagrant 4y ago
      > Fair warning: everything I know about orbital mechanics is from Kerbal Space Program. Knowing what I know about that game I read this as: Warning; I actually know what I'm talking about here.
      - cwillu 4y ago
- chowells 4y ago
  If the moon's orbit is increasing in radius, doesn't that mean its orbital velocity is decreasing? Which way is energy being transferred? This stuff confuses me.
  - ncallaway 4y ago
    I haven't done the math, but I strongly suspect that the potential energy (from moving away from the source of gravity) is increased more than the kinetic energy (from the reduced velocity) decreases. So, I would think when the moon moves away from the earth, its total energy increases. Thus, the earth's energy decreases (in the form of slightly reduced rotational kinetic energy)
    - onos 4y ago
      That’s right. The radius is set by the force mv^2/r = GMm/r^2. —> mv^2/2 = 0.5 GMm/r —> Kinetic plus potential = - 0.5 GMm/r This goes up with r.
    - sliken 4y ago
      Earths rotational velocity is decreased (longer days) and added to the moon which increases it's potential energy (distance relative to earth), increases it's orbital height, and increases the period of it's orbit (the lunar month). But once the lunar month = earth day the transfer will stop and the moon will slowly approach earth again, until it hits the roche limit and becomes a ring.
  - sgtnoodle 4y ago
    Its relative velocity with respect to a Cartesian frame of reference fixed on the surface of the Earth may be dropping, but that's not particularly meaningful. Think of the moon being in free fall, without any external forces acting on it. It would be moving at a constant velocity in a straight line, except the space and time it is in is curved due to gravity. Because of that curved spacetime, the moon appears to accelerate relative to the Earth. It's not actually accelerating, though; it is moving in a straight line at a constant velocity, the straight line just happens to be curved completely around the Earth. The tidal forces are literal forces, and forces cause acceleration. So, the moon isn't quite moving at constant velocity. The change in velocity means the moon isn't quite travelling in a straight line through spacetime. The orbit changes, and in this case gets higher and slower relative to the Earth. Another way to think about it. If you're in a space ship at a point X1 in an orbit, you can steer the nose of the ship in the direction you're moving relative to the Earth, and fire your rocket engine. You're now going faster. The opposite end of your orbit, point Y1, will now be higher in altitude than it would have otherwise been. Your relative speed at Y1 will indeed be slower than where you would have been had you not fired your engine, but when you circle back to X1 again your speed will still be higher. When you get to Y1 again, you could fire your engine a second time and increase your speed even more. You'll no longer end up back at X1, but a new point X2 at a higher altitude than X1 was. Your relative velocity at X2 will be lower than it was at X1. In space, "speed" isn't really velocity, but acceleration. Big rocket engines make you go fast! In The Martian, the main character makes a comment to that effect when he talks about NASA convincing him to strap himself into a hodge podge death rocket, by claiming he'll be the "fastest" astronaut in history. In a future where humans practically travel to a distant star, a "fast enough" space ship would be one that can maintain constant non-trivial acceleration for many decades. You would accelerate to the halfway point, then turn around and decelerate the rest of the way. Assuming you got fast enough relative to the destination, weird relativistic effects would become obviously apparent and the travellers would perceive space and time compressing.
deleted 4y ago
[deleted]
Manu40 4y ago
I was recently looking at some data about day lengths, and basically it all boils down to the fact that the earth doesn't orbit the sun in a perfect circle, which causes slight accelerations and decelerations; along with its wobble. That wobble as I understand is due to the effect of tidal forces due to the moons pull on our ocean. Tropical/Solar days = 24 hours But Sidereal = 23 h 56 min 4.0905 seconds Why the difference? Because of those prior mentioned forces causing the location of the sun to be slightly out of alignment from where it started the day prior. Or something like that. Tropic/Solar days are determined by the position of the sun, as per the name. Sidereal are based upon the position of the stars. or so I understand. To be clear. I am not an expert. I am just regurgitating what I read from NASA.
- Telemark70 4y ago
  The difference between the solar day and the sidereal day is caused solely by the progress of the earth in its orbit. After 23 hours 56 minutes the earth has made a full rotation relative to the stars. But it has to turn for a further 4 minutes to get the sun to be above the same place on the earth. The difference between the day lengths is one day divided the number of days in a year, i.e. approximately 24 hours / 365.
  - Manu40 4y ago
    Yeah, that's basically exactly what I said but with different words. Also, wobble does play a factor. You may want to look into it again some more. https://singularityhub.com/2022/08/07/the-length-of-earths-days-has-been-mysteriously-increasing-and-scientists-dont-know-why/#:~:text=Apart%20from%20these%20large%2Dscale,a%20millisecond%20in%20either%20direction https://singularityhub.com/2022/08/07/the-length-of-earths-d.... > Apart from these large-scale changes, over shorter periods weather and climate also have important impacts on Earth's rotation, causing variations in both directions. The fortnightly and monthly tidal cycles move mass around the planet, causing changes in the length of day by up to a millisecond in either direction.
raducu 4y ago
> wish they explained why the moon being that much closer would have such a dramatic effect on the day length. Can someone explain this? Seems off to me, but I'm very physics-naive Earth-Moon momentum is conserved. Think of a pregnant woman (the Earth) spinning on a seivel chair. The woman gives birth to her child (the Moon) and she takes the child in her arms and extends it at arm's length. Their rotation slows down, just like an iceskater slows down when spinning and extending their arms. The Earth does not have phisical arms holding the Moon, but it has gravity and the Moon also has gravity that affects the ocean tides -- the tidal effects are like tiny tiny arms that both the Earth and the Moon use to push eachother away (and lose a lot of energy in the process also). The Earth is losing rotational momentum at the expense of the Moon, which is gaining momentum and increasing speed in traveling around the Earth which increases the centrifugal force which means the Moon goes to a higher and higher orbit and further and further away from Earth.
- SJSque 4y ago
  > Think of a pregnant woman (the Earth) spinning on a seivel chair. The woman gives birth to her child (the Moon) and she takes the child in her arms and extends it at arm's length. Just in case any of you were thinking of patenting this idea, I'm afraid that someone beat you to it: https://patents.google.com/patent/US3216423A/en https://patents.google.com/patent/US3216423A/en
vikingerik 4y ago
That explanation is worded somewhat backwards as for cause and effect. It's not that the moon being closer caused the day to be shorter. It's that if we extrapolate backwards from the current values of the day length and the rate of slowing, we calculate that the day must have been 17 hours back then. The cause-and-effect is that the 17-hour rotational period became 24 hours by tidal deceleration. Other posts have given the cause - conservation of angular momentum in the Earth-Moon system. Angular momentum transfers from the Earth's rotation to the Moon's orbit. If what you're concerned about is the magnitude of the effect, that's pretty well explainable - the planet now rotates 25% slower when the moon is 25% farther.

mgraczyk 4y ago

To first order I think the explanation is just conversation of angular momentum. The moon earth system has to have it's angular momentum constant over time. If the moon is further away in a stable orbit, the earth must rotate slower.

morsch 4y ago

It's explained here: https://en.m.wikipedia.org/wiki/Tidal_acceleration https://en.m.wikipedia.org/wiki/Tidal_acceleration

FiatLuxDave 4y ago

Sure. The earth is spinning faster than the the moon is going around the earth (earth rotates in one day, the moon goes around in about a month). When the tides transfer energy and momentum to the moon from the earth's spin, it slows down the earth's spin and gives the moon more energy. This moves the moon to a higher orbit, so it moves a bit farther away from us. The source of energy for the whole process is the earth's spin. It takes a lot of energy to lift a moon, relative to the amount of energy in the earth's spin, which is why it has such a dramatic effect on the day length.

redact207 4y ago
If the moon wasn't drifting away and was in a static orbit, would the Earth's rotation slow and the moon's orbit speed up to the point where they're in sync?
- yellowapple 4y ago
  Eventually, yeah; just as the Moon is tidally locked to Earth, Earth would be tidally locked to the Moon. I don't know offhand whether that would happen before the Moon drifts too far away to remain in Earth's orbit, however.
  - sliken 4y ago
    Moon is below escape velocity, so it's not leaving. In fact when 1 day = 1 lunar month the movement away will stop, and reverse. It will continue to get closer to earth until it hits the Roche limit and becomes a ring.
- aussieshibe 4y ago
  Fair warning: everything I know about orbital mechanics is from Kerbal Space Program. The moon cannot orbit at a higher speed while keeping the same semi-major axis (average distance to the orbital centre of mass). If you suddenly doubled the orbital speed of the moon right now, the apoapsis (the highest point in its orbit relative to the orbital centre of mass) would increase significantly. If you slowly accelerate the moon in the direction of its orbital velocity consistently over a long time period, the moon will slow down relative to the Earth, but it's semi major axis will increase. Actual scientists of HN: have at me.
  - incompatible 4y ago
    Yeah, the moon isn't "drifting away" on its own, its being forced away as it takes energy from the Earth.
  - robertlagrant 4y ago
    > Fair warning: everything I know about orbital mechanics is from Kerbal Space Program. Knowing what I know about that game I read this as: Warning; I actually know what I'm talking about here.
    - cwillu 4y ago
chowells 4y ago
If the moon's orbit is increasing in radius, doesn't that mean its orbital velocity is decreasing? Which way is energy being transferred? This stuff confuses me.
- ncallaway 4y ago
  I haven't done the math, but I strongly suspect that the potential energy (from moving away from the source of gravity) is increased more than the kinetic energy (from the reduced velocity) decreases. So, I would think when the moon moves away from the earth, its total energy increases. Thus, the earth's energy decreases (in the form of slightly reduced rotational kinetic energy)
  - onos 4y ago
    That’s right. The radius is set by the force mv^2/r = GMm/r^2. —> mv^2/2 = 0.5 GMm/r —> Kinetic plus potential = - 0.5 GMm/r This goes up with r.
  - sliken 4y ago
    Earths rotational velocity is decreased (longer days) and added to the moon which increases it's potential energy (distance relative to earth), increases it's orbital height, and increases the period of it's orbit (the lunar month). But once the lunar month = earth day the transfer will stop and the moon will slowly approach earth again, until it hits the roche limit and becomes a ring.
- sgtnoodle 4y ago
  Its relative velocity with respect to a Cartesian frame of reference fixed on the surface of the Earth may be dropping, but that's not particularly meaningful. Think of the moon being in free fall, without any external forces acting on it. It would be moving at a constant velocity in a straight line, except the space and time it is in is curved due to gravity. Because of that curved spacetime, the moon appears to accelerate relative to the Earth. It's not actually accelerating, though; it is moving in a straight line at a constant velocity, the straight line just happens to be curved completely around the Earth. The tidal forces are literal forces, and forces cause acceleration. So, the moon isn't quite moving at constant velocity. The change in velocity means the moon isn't quite travelling in a straight line through spacetime. The orbit changes, and in this case gets higher and slower relative to the Earth. Another way to think about it. If you're in a space ship at a point X1 in an orbit, you can steer the nose of the ship in the direction you're moving relative to the Earth, and fire your rocket engine. You're now going faster. The opposite end of your orbit, point Y1, will now be higher in altitude than it would have otherwise been. Your relative speed at Y1 will indeed be slower than where you would have been had you not fired your engine, but when you circle back to X1 again your speed will still be higher. When you get to Y1 again, you could fire your engine a second time and increase your speed even more. You'll no longer end up back at X1, but a new point X2 at a higher altitude than X1 was. Your relative velocity at X2 will be lower than it was at X1. In space, "speed" isn't really velocity, but acceleration. Big rocket engines make you go fast! In The Martian, the main character makes a comment to that effect when he talks about NASA convincing him to strap himself into a hodge podge death rocket, by claiming he'll be the "fastest" astronaut in history. In a future where humans practically travel to a distant star, a "fast enough" space ship would be one that can maintain constant non-trivial acceleration for many decades. You would accelerate to the halfway point, then turn around and decelerate the rest of the way. Assuming you got fast enough relative to the destination, weird relativistic effects would become obviously apparent and the travellers would perceive space and time compressing.

deleted 4y ago

[deleted]

Manu40 4y ago

I was recently looking at some data about day lengths, and basically it all boils down to the fact that the earth doesn't orbit the sun in a perfect circle, which causes slight accelerations and decelerations; along with its wobble. That wobble as I understand is due to the effect of tidal forces due to the moons pull on our ocean. Tropical/Solar days = 24 hours But Sidereal = 23 h 56 min 4.0905 seconds Why the difference? Because of those prior mentioned forces causing the location of the sun to be slightly out of alignment from where it started the day prior. Or something like that. Tropic/Solar days are determined by the position of the sun, as per the name. Sidereal are based upon the position of the stars. or so I understand. To be clear. I am not an expert. I am just regurgitating what I read from NASA.

Telemark70 4y ago
The difference between the solar day and the sidereal day is caused solely by the progress of the earth in its orbit. After 23 hours 56 minutes the earth has made a full rotation relative to the stars. But it has to turn for a further 4 minutes to get the sun to be above the same place on the earth. The difference between the day lengths is one day divided the number of days in a year, i.e. approximately 24 hours / 365.
- Manu40 4y ago
  Yeah, that's basically exactly what I said but with different words. Also, wobble does play a factor. You may want to look into it again some more. https://singularityhub.com/2022/08/07/the-length-of-earths-days-has-been-mysteriously-increasing-and-scientists-dont-know-why/#:~:text=Apart%20from%20these%20large%2Dscale,a%20millisecond%20in%20either%20direction https://singularityhub.com/2022/08/07/the-length-of-earths-d.... > Apart from these large-scale changes, over shorter periods weather and climate also have important impacts on Earth's rotation, causing variations in both directions. The fortnightly and monthly tidal cycles move mass around the planet, causing changes in the length of day by up to a millisecond in either direction.

raducu 4y ago

> wish they explained why the moon being that much closer would have such a dramatic effect on the day length. Can someone explain this? Seems off to me, but I'm very physics-naive Earth-Moon momentum is conserved. Think of a pregnant woman (the Earth) spinning on a seivel chair. The woman gives birth to her child (the Moon) and she takes the child in her arms and extends it at arm's length. Their rotation slows down, just like an iceskater slows down when spinning and extending their arms. The Earth does not have phisical arms holding the Moon, but it has gravity and the Moon also has gravity that affects the ocean tides -- the tidal effects are like tiny tiny arms that both the Earth and the Moon use to push eachother away (and lose a lot of energy in the process also). The Earth is losing rotational momentum at the expense of the Moon, which is gaining momentum and increasing speed in traveling around the Earth which increases the centrifugal force which means the Moon goes to a higher and higher orbit and further and further away from Earth.

SJSque 4y ago
> Think of a pregnant woman (the Earth) spinning on a seivel chair. The woman gives birth to her child (the Moon) and she takes the child in her arms and extends it at arm's length. Just in case any of you were thinking of patenting this idea, I'm afraid that someone beat you to it: https://patents.google.com/patent/US3216423A/en https://patents.google.com/patent/US3216423A/en

vikingerik 4y ago

That explanation is worded somewhat backwards as for cause and effect. It's not that the moon being closer caused the day to be shorter. It's that if we extrapolate backwards from the current values of the day length and the rate of slowing, we calculate that the day must have been 17 hours back then. The cause-and-effect is that the 17-hour rotational period became 24 hours by tidal deceleration. Other posts have given the cause - conservation of angular momentum in the Earth-Moon system. Angular momentum transfers from the Earth's rotation to the Moon's orbit. If what you're concerned about is the magnitude of the effect, that's pretty well explainable - the planet now rotates 25% slower when the moon is 25% farther.