Save the Moon Math Challenge: How much energy required to cancel Moon's expanding orbit?

[darthgently]

I'm bored so I'm going to stir the pot.   The Moon is slowly expanding its orbit due to Earth/Moon tidal forces emerging from differences in Earth's rotational period and Lunar orbital period.   Yes I know the Moon won't ever completely escape the Earth without some outside influence but in a mere 50 billion years the Earth-Moon distance will have grown to the point that they will be completely tidally locked to one another with Earth's rotational period matching the Moon's orbital period such that each takes about 47 current day's worth of time.  This is undesirable and unacceptable.   Who wants a to work a 360 hour shift (1/3 of the new "day")?

How much energy ( +/-  1% ) per second constantly applied would it take to halt the increasing average distance from the Earth to the Moon?

Bonus Question:  How would you recommend applying this energy?  Huge pumps moving the oceans around?  Flippable light absorbing/reflecting panels completely covering most of the lunar surface?  Moar boosters?

 

Edited March 22, 2022 by darthgently

[SunlitZelkova]

How to save the Moon? Change your perception of what constitutes salvation.

Let the Moon be the Moon. It deserves to go out (further) in to the universe and try new things. Same goes for members of the genus homo, if it can survive for that long.

[darthgently]

1 hour ago, SunlitZelkova said:

How to save the Moon? Change your perception of what constitutes salvation.

Let the Moon be the Moon. It deserves to go out (further) in to the universe and try new things. Same goes for members of the genus homo, if it can survive for that long.

I feel bad you took the question so seriously.  But interesting answer.  One point awarded.

[SunlitZelkova]

Just now, darthgently said:

I feel bad you took the question so seriously.  But interesting answer.  One point awarded.

It was actually a sort of half-joke. If I was a human or intelligent Earth inhabitant 50 billion years from now, I wouldn't care that much about the Moon's or Earth's rotational period. But on the other hand if we bring Late Holocene homo sapiens behavioral matters into the question (like "over work" and "disliking work") then a philosophical response is what immediately comes to mind, rather than engineering. I decided to dress it up in a manner similar to some parenting debates though.

After all, the Moon is only in a bad position if we think the Moon is in a bad position.

[RCgothic]

Orbital energy is the sum of kinetic and potential energy.

Potential energy= m*g*Dh

Mass of the moon is 7.34767E22kg.

Earth's gravity at lunar radius is given by GM/r^2

Moon's radius is 385000km. Earth's GM is 3.986E14m3/s2. So g at lunar radius is 2.689mm/s/s.

And dh is 38mm/y.

Potential energy is therefore increasing at 7.5E18 J/year.

Kinetic energy is 0.5mv^2. 

Orbital v is given by SQRT(GM/r) = 1017.5m/s at 385000km, or 1017.5m/s at 385000km and 38mm. In fact the difference in orbital velocity is just 0.05nm/s.

But in fact this amounts to a kinetic energy difference of -3.75E18 J/year.

So by adding the two (one is negative) you'd need to add 3.75E18 J/year (119 TeraWatts) to halt the moon's recession.

And probably the same again to earth to replenish lost rotational energy.

Currently earthly civilization consumes a total of 18TW from all sources.

Edited March 22, 2022 by RCgothic

[RCgothic]

Also, interestingly, Saturn V produces 38.85MN of vacuum thrust. Placed on the moon facing retrograde at lunar orbital velocity of 1017m/s, that develops about 40GW of power.

So it'd take just 3 Saturn S-ICs placed on the moon and thrusting continuously to keep it in its place.

Crazy how a single Saturn V in flight eclipses total global power consumption! That sounds like a fact that can't possibly be true, but apparently is.

Could actually be a real problem if Superheavy starts flying anything even close to hourly.

Edit: MN multiplied by 1000m/s is GW, not TW. I'm off my a factor of 1000. >.<

Edited April 5, 2022 by RCgothic

[darthgently]

11 minutes ago, RCgothic said:

Also, interestingly, Saturn V produces 38.85MN of vacuum thrust. Placed on the moon facing retrograde at lunar orbital velocity of 1017m/s, that develops about 40TW of power.

So it'd take just 3 Saturn S-ICs placed on the moon and thrusting continuously to keep it in its place.

Crazy how a single Saturn V in flight eclipses total global power consumption! That sounds like a fact that can't possibly be true, but apparently is.

Could actually be a real problem if Superheavy starts flying anything even close to hourly.

That is an eye-opener.  I'm taking your inputs and calcs at face value.  Now I'm wondering if 119 TW (or half that?) of energy were harvested on Earth from tidal energy (somehow magically) if the lunar recession would not occur, or be greatly lessened.  Nip it in the bud

I like the image of 12 F1 engines burning continuously forever though (virtually forever)

Edited March 22, 2022 by darthgently

[RCgothic]

It'd be 15 F1 engines, although it could probably be less with vacuum nozzles!

I've run some numbers on Superheavy though. Assuming 33 engines at full thrust, similar burn time to F9 (162s), and similar CECO or downthrottle to Saturn V at 2.1km/s, Superheavy will develop 156GW of power.

Assuming a triangular power profile (starts at 0, increases linearly to max), that's ~80GW over the entire flight.

With 3 flights an hour (hourly turnaround), Superheavy will operate for 468s (3x162s)of every 3600s long hour. That's an aspiration to an average developed power of ~10GW.

 

Is it a problem that SpaceX plans to increase global power consumption by ~55%?

Or are these just fantasy numbers that aren't apples to apples because rockets are extremely efficient at converting thrust into power and most of civilization isn't? I don't actually know.

Edit: numbers were off by a factor of 1000.

Edited April 5, 2022 by RCgothic

[Gargamel]

8 hours ago, SunlitZelkova said:

If I was a human or intelligent Earth inhabitant 50 billion years from now, I wouldn't care that much about the Moon's or Earth's rotational period.

By some estimates, they won’t even exist then.   By most of the rest, they’ll just be charred rocks.  

[Terwin]

17 hours ago, darthgently said:

I'm bored so I'm going to stir the pot.   The Moon is slowly expanding its orbit due to Earth/Moon tidal forces emerging from differences in Earth's rotational period and Lunar orbital period.   Yes I know the Moon won't ever completely escape the Earth without some outside influence but in a mere 50 billion years the Earth-Moon distance will have grown to the point that they will be completely tidally locked to one another with Earth's rotational period matching the Moon's orbital period such that each takes about 47 current day's worth of time. 

 

6 hours ago, Gargamel said:

By some estimates, they won’t even exist then.   By most of the rest, they’ll just be charred rocks.  

What is the expected change in the 5BY we are expected to have before the sun swallows both?

 

Was do we think the orbit of the moon/rotation of the earth was ~4.5BY ago when they formed a stable system? 

[darthgently]

9 hours ago, Gargamel said:

By some estimates, they won’t even exist then.   By most of the rest, they’ll just be charred rocks.  

So you are saying you'd rather work a 360 hour work shift on a charred rock than answer the question.  Minus 1 point.

[kerbiloid]

1 hour ago, darthgently said:

Minus 1 point.

Just "minus 1 point"??? Ban him!

1 hour ago, darthgently said:

work shift on a charred rock

Why work? Play.

Spoiler

 

 

50 bln years later the world will be a fantasy like this one.

[magnemoe]

19 hours ago, RCgothic said:

Also, interestingly, Saturn V produces 38.85MN of vacuum thrust. Placed on the moon facing retrograde at lunar orbital velocity of 1017m/s, that develops about 40TW of power.

So it'd take just 3 Saturn S-ICs placed on the moon and thrusting continuously to keep it in its place.

Crazy how a single Saturn V in flight eclipses total global power consumption! That sounds like a fact that can't possibly be true, but apparently is.

Could actually be a real problem if Superheavy starts flying anything even close to hourly.

Saturn 5 used 20 ton fuel each second, and it was burning it with oxygen, not air but that should not matter that much for energy produced. 
if it burned for 4 hours it would use 288.000 ton fuel, so you needed to feed it 6 supertankers every day. 
However stopping the moon sounds pretty plausible with an large orion pulse nuclear engine. Stopping Earth from slowing down would be harder. 

[Gargamel]

10 hours ago, darthgently said:

So you are saying you'd rather work a 360 hour work shift on a charred rock than answer the question.  Minus 1 point.

Ahhhhhh a short work week... sounds wonderful.   I’ll take the point hit.  

[Nuke]

On 3/22/2022 at 3:12 PM, darthgently said:

That is an eye-opener.  I'm taking your inputs and calcs at face value.  Now I'm wondering if 119 TW (or half that?) of energy were harvested on Earth from tidal energy (somehow magically) if the lunar recession would not occur, or be greatly lessened.  Nip it in the bud

I like the image of 12 F1 engines burning continuously forever though (virtually forever)

if we start tapping tidal energy it should in theory have a slow barely measurable (unless taken to some extreme) effect on the moon. im not sure if it would reel it in or out. but you are adding resistance to a natural process. i have a similar concern about geothermal. you start tapping core, you accelerate the cooling down of the planet interior and the inevitable shutting down its magneto. 

[darthgently]

3 hours ago, Nuke said:

if we start tapping tidal energy it should in theory have a slow barely measurable (unless taken to some extreme) effect on the moon. im not sure if it would reel it in or out. but you are adding resistance to a natural process. i have a similar concern about geothermal. you start tapping core, you accelerate the cooling down of the planet interior and the inevitable shutting down its magneto. 

Don't forget that much of the heat of the core comes from tidal forces in the magma itself which would be pretty hard to tap.  I recall some comes from radiactive decay also.  As the Moon gets further away it also lessens the lifespan of the terrestrial magneto.  Damned if you do, damned if you don't

[magnemoe]

On 3/27/2022 at 1:11 PM, Nuke said:

if we start tapping tidal energy it should in theory have a slow barely measurable (unless taken to some extreme) effect on the moon. im not sure if it would reel it in or out. but you are adding resistance to a natural process. i have a similar concern about geothermal. you start tapping core, you accelerate the cooling down of the planet interior and the inevitable shutting down its magneto. 

Don't think tapping tidal affect the moon more than solar panels affect the sun as in the sun don't care if its inside an dyson swarm. 
You are just using an energy gradient same as an water wheel, yes the dam will have local effects like fish not getting upstream of your dam but no global ones. 
 

[magnemoe]

On 3/27/2022 at 4:56 PM, darthgently said:

Don't forget that much of the heat of the core comes from tidal forces in the magma itself which would be pretty hard to tap.  I recall some comes from radiactive decay also.  As the Moon gets further away it also lessens the lifespan of the terrestrial magneto.  Damned if you do, damned if you don't

My apartment block is heated from ground heat. Yes it use electricity but you get 5 times the heat out of it compared to an electric heater. 
Yes its mostly feed of the ground water from an small river but is still its taping deep heat. 

Now getting power out of it is much harder as you need to generate enough power to run an steam turbine efficient enough 

[RCgothic]

21 minutes ago, magnemoe said:

Don't think tapping tidal affect the moon more than solar panels affect the sun as in the sun don't care if its inside an dyson swarm. 
You are just using an energy gradient same as an water wheel, yes the dam will have local effects like fish not getting upstream of your dam but no global ones. 
 

I think theoretically tapping tidal power reduces the size of the tidal bulge - it offers additional resistance to the tidal deformation.

A smaller tidal bulge will subsequently exert less torque on the moon.

But I believe most of the tidal effect on the moon comes from deformation of earth's mantle, not its oceans. It's pretty inconceivable humanity could tap enough tidal energy for the moon to notice.

[darthgently]

1 hour ago, magnemoe said:

Don't think tapping tidal affect the moon more than solar panels affect the sun as in the sun don't care if its inside an dyson swarm. 
You are just using an energy gradient same as an water wheel, yes the dam will have local effects like fish not getting upstream of your dam but no global ones. 

None of the analogies you use work the same as gravity.  In fact the movement of water on Earth does accelerate the Moon using gravity, which works in two directions.  Photons from the sun and the water in the dam scenario only flows one direction.  Gravity works both ways and the tidal movement hysteresis introduces a lag in the loop that accelerates the Moon.  Because the tidal bulge is out of phase, combined with the Earth's rotation, their grav effects make this happen even if the Moon helped create the initial force.  Tapping energy from the tidal effect would decrease the tidal force affecting the Moon

Think of it as the tidal energy tapping as a filter in the feedback loop tuned to the resonance of the "circuit" so there ends up being less positive feedback in the loop

Edited March 30, 2022 by darthgently

[RCgothic]

I'm sorry, I made a maths error earlier. MN multiplied by km/s is GW, not TW. I was off by a factor of 1000. >.<