Editing Openai/690f6231-2acc-8000-9a21-b358ecd8ce70

{{ChatGPT Share}}
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|id=690f6231-2acc-8000-9a21-b358ecd8ce70
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|created=20251109031959
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== 对话内容 ==

= Moon parking and day length =
''Generated: 2025-11-08 22:17:41''

'''Prompt:'''
Would parking a moon in earths orbit make the day longer?

'''ChatGPT:'''
Yes — adding another moon (or “parking” one) in Earth’s orbit could make Earth’s day longer over time, but not immediately.

Here’s why:

* The tidal interaction between Earth and its moon transfers rotational energy from Earth to the moon’s orbit. This slows Earth’s rotation slightly while pushing the moon farther away.
* If you add another sizable moon, it would generate additional tidal forces, further enhancing that braking effect.
* The magnitude depends on the new moon’s mass and distance — a large, close moon would noticeably increase the rate of tidal braking; a small or distant one would barely matter.

So:

* Short-term (immediate): The day wouldn’t suddenly lengthen.
* Long-term (millions of years): Yes, the day would gradually become longer, just as Earth’s current 24-hour day used to be about 18 hours long when the Moon was much closer.

Would you like a rough estimate of how much longer the day could get for a second moon of a given size?


'''Prompt:'''
Yes, I would like to make the day an hour longer.

'''ChatGPT:'''
Nice — let’s make the day exactly 1 hour longer (24 → 25 h). I’ll show the physics, a simple calculation, and what it means in plain terms.

What has to change

* Earth’s rotation has to lose angular momentum. To slow the 24-hour spin to 25 hours Earth must lose

ΔL≈2.33×1032 kg\cdotpm2/s.\Delta L \approx 2.33\times10^{32}\ \text{kg·m}^2/\text{s}.ΔL≈2.33×1032 kg\cdotpm2/s.
How to store that angular momentum in a moon

* The orbital angular momentum of a circular satellite is Lorb=mGM⊕aL_{\rm orb}=m\sqrt{G M_\oplus a}Lorb=mGM⊕a.
* If you give the entire ΔL\Delta LΔL to a single parked moon at orbital radius aaa, its mass would need to be

m≈∣ΔL∣GM⊕a.m \approx \frac{|\Delta L|}{\sqrt{G M_\oplus a}}.m≈GM⊕a∣ΔL∣.
Using that formula for three representative parking radii:

* Near current Moon distance (a ≈ 384,400 km): → m≈6.0×1020m \approx 6.0\times10^{20}m≈6.0×1020 kg (≈ 0.8% of the Moon’s mass) If made of rock (~3000 kg/m³) that’s a spherical body ≈ 720 km diameter (roughly Ceres-sized).
* Geostationary radius (a ≈ 42,164 km): → m≈1.8×1021m \approx 1.8\times10^{21}m≈1.8×1021 kg (≈ 2.4% of Moon’s mass) — bigger, because closer orbits carry less angular momentum per kg.
* Low Earth orbit (7000 km): → m≈4.4×1021m \approx 4.4\times10^{21}m≈4.4×1021 kg (≈ 6% of Moon’s mass) — impractically large and also unstable / destructive for LEO.

Interpretation & important caveats

* Those numbers show how much orbital angular momentum is required to change the day by one hour. A single object roughly the mass/size of a large dwarf planet (hundreds of km radius) placed at lunar distance contains about the right orbital angular momentum.
* But placing such an object in orbit does not automatically slow Earth instantly unless the angular momentum is transferred from Earth into that object. How the transfer happens matters: * If you could magically assemble the moon already carrying that orbital angular momentum (i.e., bring it in from far away with the required L and park it), Earth’s rotation would change by conservation of total angular momentum — the numbers above apply directly. * If instead you “park” a body and expect tides to do the work, tidal exchange is usually very slow — it could take millions of years unless the moon is massive and/or very close (which brings huge stability and safety problems).
* Real-world complications: three-body dynamics with the existing Moon, orbital resonances, tidal heating, long-term orbital stability, collision risk, and changes to tides/climate. A body hundreds of km across in near-Earth space would be a massive hazard.

Short takeaway: to gain one extra hour you need to remove ≈ 2.33×10322.33\times10^{32}2.33×1032 kg·m²/s from Earth’s spin. That is comparable to giving that angular momentum to a moon roughly 6×10²0 kg if parked at the current Moon’s distance — roughly a ~700 km diameter rocky body. Whether you achieve that by magically placing such a moon (instant effect) or by slow tidal braking (very slow) changes the feasibility and consequences dramatically.

Want me to:

* convert those masses to familiar objects (Ceres / big asteroids), or
* estimate how long tidal transfer would take for a given moon mass and distance (I can do a rough timescale estimate next)?


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