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This question is about an Earth-like planet that doesn't rotate around its own axis.

Normally the sun and moon rotate around the planet, providing a day/night cycle, but this has stopped for reasons. Now the sun, earth and moon are locked in a line. The earth doesn't turn, and neither does the moon circle around the planet. This means that one side is constantly lit up, while the other side has the moon but is in constant darkness.
Tidally locked planet, with the tidally locked moon in a line.
Simple drawing of the situation, not to scale.

To recreate a day-night cycle, the plan is to rotate the planet instead of spinning the sun/moon around it. The small problem is that there currently is a civilization living on the planet, and they'd rather not be thrown off it. In fact, the civilization would rather not be significantly discomforted by the acceleration of the planet. Discomfort such as buildings collapsing, or parts of the civilization dying/being noticeably affected by the acceleration.

How long would it take for a tidally locked planet to be accelerated to spin around its own axis -similar to Earth- to reach Earth's rotation speed if we want to keep problems the acceleration causes to a minimum?

While I am looking for a more exact answer, a ballpark would be enough. could it be set up to happen in a few seconds? a minute? hour? day?

To preempt the questions:

  • The planet, sun, and moon are about as big as ours.
    • If this isn't enough, they can be considered the same size.
  • The planet is sped up by exerting force on the entire planet at the same time. Magic.
    • *This does not include inhabitants or constructs.
  • Yes this question is about the mlp planet Equus.
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    $\begingroup$ In our universe, a star can’t orbit a planet. Technically, they both orbit their barycenter, but since the barycenter is usually inside the star, we simplify that to say the plant orbits the star. If this is not how physics works in your universe, you will need to specify how it does work. $\endgroup$
    – StephenS
    Commented Aug 9, 2022 at 14:09
  • $\begingroup$ It is the My Little Pony (FiM) universe. The sun and moon are basically dragged around the planet with magic, to create a day-night cycle. In the series, it is implied that the sun and moon need to be moved constantly to keep this day-night cycle. While it is also said the sun/moon/planet are as big as ours. Now how the rotation of the planet is accelerated doesn't matter. (it could be magic?) I avoided the hard-science tag for a reason. The question is about how fast the planet can safely be spun up to match our Earth's rotation, without harming the population. $\endgroup$
    – vinzzz001
    Commented Aug 9, 2022 at 15:25
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    $\begingroup$ Shorter version: My world has extremely powerful magic which completely defies physics as we have known it for four centuries. How fast can my almost all-powerful magic perform a magic trick? $\endgroup$
    – AlexP
    Commented Aug 9, 2022 at 15:34
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    $\begingroup$ @AlexP Kinda, but not really. Rather than that, most of the things in question don't matter. The method of acceleration, the starting position of the sun/moon/earth, or how they got there, all could be considered fluff. I am only interested in the time it would take for an Earth-like planet to be spun up to Earth-like rotational velocity, without flinging people off the surface, buildings crumbling because of sideways force, or granny dying because she couldn't resist the sudden change in G-forces. $\endgroup$
    – vinzzz001
    Commented Aug 9, 2022 at 21:02
  • $\begingroup$ @vinzzz001 I don't understand why people are giving you such a hard time about parameterising your problem tightly and asking to ignore other issues. $\endgroup$
    – user86462
    Commented Aug 11, 2022 at 1:40

3 Answers 3

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What you have detailed is a physically impossible situation: the only way for two bodies to be at rest with respect to each other while orbiting around a third one is for them to have the same orbit. Also if the moon was at rest with respect to the planet, it would soon fall onto it because of that thing called gravity.

Therefore, since the moon will be orbiting around the planet, this rotation will very slowly put the planet in rotation until a tidal locking is reached. That would take a very very long time. Consider that our Earth has not yet reached tidal locking with Moon in 4.5 billion years.

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  • $\begingroup$ Would it help if the earth and moon both orbited the sun, tidally locked to it? I would be willing to remove the moon being similar in size/mass if it would allow it to cancel out both the pull of the sun and earth on the moon to allow for its placement, even if the sun-planet-moon alignment can only be kept as a temporary state. $\endgroup$
    – vinzzz001
    Commented Aug 9, 2022 at 13:16
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    $\begingroup$ @vinzzz001 That wouldn’t help. If they’re in the same orbit, gravity will eventually pull them together. The only reason our moon doesn’t fall to the earth is that it is in orbit around us, i.e. it is falling at such an angle that it keeps missing us, rather than around the sun. $\endgroup$
    – StephenS
    Commented Aug 9, 2022 at 14:06
  • $\begingroup$ Could this not work if the moon in this situation were located near L2 of the Sun-Earth system? It would be an unstable equilibrium, but an equilibrium nonetheless. $\endgroup$
    – OrOrg
    Commented Aug 10, 2022 at 7:44
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    $\begingroup$ @OrOrg The Earth-Sun L2 is so far away I doubt we’d even see the moon. You might as well redefine things so the (much smaller) sun was in the same orbit as the moon, with minimal magic to keep them 180° out of phase. And a bit more magic to keep a sun that tiny still burning, of course. $\endgroup$
    – StephenS
    Commented Aug 10, 2022 at 17:50
  • $\begingroup$ @StephenS Sun-Earth L1 and L2 are about four times as far as the Moon. $\endgroup$
    – Anton Sherwood
    Commented Aug 29, 2022 at 4:47
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The main problem is the ocean.

The people can handle a little acceleration. I doubt the air is that big a deal either, though high winds are to be expected. But if your planet has a few kilometers depth of ocean that didn't get the memo, you're at risk of taking a bath.

The radius isn't specified, so this isn't going to be a precise answer. I'm not so keen on calculating the effect of friction on the ocean anyway. But picture a flat 3000 km width of ocean, and now you accelerate it sideways at 1/100 g. Then the direction of "down" shifts by 1%. One end of your ocean is liable to fall by 15 km and the other end to rise by 15 km. You might want to reduce the sea level rise to something more like 15 meters (wait a few decades and we'll see what that looks like first hand). But then you're only accelerating at 1/100,000 g!

Good news: for an Earth-sized world with an Earth-length day we only need to accelerate the equator to 1700 km/hr = 460 m/s. So 0.000098 m/s^2 will get you there in 4.7 million seconds = 54 days.

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  • $\begingroup$ Would the shift in water level happen as a gradual shift such as the tides that keeps getting higher, or am I to expect something like a coast-wide tidal wave/storm surge/tsunami? $\endgroup$
    – vinzzz001
    Commented Aug 11, 2022 at 9:11
  • $\begingroup$ A tsunami is a very gradual shift at sea, but it does indeed become abrupt at the land. I'm not sure how to determine if there is a way to adjust the precise way in which acceleration begins, which would reduce the abruptness of the sea level rise. $\endgroup$
    – Mike Serfas
    Commented Aug 11, 2022 at 22:55
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Earth’s rotation is roughly 1000 mph. At a constant acceleration of 1 mph per second, it would take 1000 hours (just under 42 days) to reach proper rotation speed. Doubling that acceleration to 2 mph per second, would decrease the time by half (21 days). 4 mph per sec = 10.4 days.

Force = Mass x Acceleration

A person with 200 lbs. of mass accelerating at 1 mph/s = 40 Newton of force, or around 9 lbs. Which means that the person will feel nine pounds of force pushing either against or with their direction of movement depending on if they are walking towards or against the rotation. Doubling the speed doubles the force. 2 mph/s = 81 Newton/18 lbs. 4 mph/s = 162 Newton/36 lbs.

You stated that constructs are not immune to the force of acceleration, so that must be taken into account. The average weight of a vehicle is 4,156. 1 mph acceleration would impart 189 lbs. of force against it, about the weight of that 200 lb. person leaning against it, so not really an issue. The weight of the Empire State Building is 365,000 tons. 365,000 x 2000 lbs. = 730,000,000 lbs. Accelerating that amount of weight at 1 mph gives us a force of 33,277,337 lbs. I am not sure if the Empire State Building can resist a sideways shear force of 33 million pounds.

If you want to reduce the impact to something negligible, you could have an acceleration of 0.114 mph/s for 365 days and get to 998.6 mph. This would reduce the shear force against the Empire State Building to 3,793,616 lbs., which is probably within tolerance if I had to guess. For comparison, this would equal 4.6 Newton/1 lb. of force against the 200 lb. person. Less than what is felt from a stiff breeze.

Edit: I used a constant acceleration calculator (https://www.ajdesigner.com/constantacceleration/cavelocity.php#ajscroll) to get the acceleration rate needed to achieve the proper speed of Earth rotation. With an initial velocity of 0, and an acceleration (in mph) and time of X. For the force calculation I used (https://www.calculatorsoup.com/calculators/physics/force.php) to calculate the mass in lbs. against acceleration in mi/(h∙s) to get the newtons of force, which can be converted into lbs of force using the same calculator.

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    $\begingroup$ Most of your calculations are meaningless or incorrect. mph is not a unit of acceleration, but just velocity. This causes all your calculations to get the wrong order of magnitude rather quickly (e.g. your 200 lbs. person would feel 0.0113 Newton of force if we assume your first paragraph to be the most correct one, not 40 Newton). Rather, mphph would correspond to what you mean but this is not a commonly used unit. $\endgroup$
    – OrOrg
    Commented Aug 10, 2022 at 7:41
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    $\begingroup$ Now, while incorrect according to the comment from OrOrg, this is the kind of answer I am looking for. $\endgroup$
    – vinzzz001
    Commented Aug 10, 2022 at 11:55
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    $\begingroup$ @Sojourner1983 acceleration is in units of distance per time per time. Mph is in units of distance per time. Notice how that when you said "accelerate at one mph" there was the implication of time. How long does it take to reach 1 mph? 1 second, one hour, one day? That's what acceleration is, the time interval to reach a speed. One could interpret an acceleration of 0.144 mph per day, but after 365 days that amounts to ~52 mph. You'll want 998.6 mph / (0.144 mph / day) to get ~6,900 days. That's about 19 years of 0.144 mph/day acceleration. $\endgroup$
    – BMF
    Commented Aug 10, 2022 at 19:18
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    $\begingroup$ @Sojourner1983 I think you're mistaken about your units. "Miles per hour" is simply not a measure of acceleration. The units just aren't there to back you up. Instantaneous acceleration is measured in units of distance over time squared. Looking through your math, I think what is being implied is miles per hour per hour, or mi/(hr^2). With that assumption, all the math checks out. $\endgroup$
    – BMF
    Commented Aug 11, 2022 at 0:58
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    $\begingroup$ @vinzzz001 I have clarified to address the mistaken impression that my math was incorrect. The links I provided will prove that the calculations I provided in my post were accurate. $\endgroup$
    – Sojourner1983
    Commented Aug 11, 2022 at 1:27

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