Inter-Orbital Kinetic Energy Exchanges: Free energy from the Outer Solar System

[YNM]

Also, there's one basic question :

If the sending and receiving bodies are different, doesn't that just mean you've moved the energy generation somewhere else ?

This isn't "free energy", this is just a transmission line. In the wrong direction.

[Mad Rocket Scientist]

3 hours ago, HebaruSan said:

How do you stop the receiver station from accelerating in the direction of the beam, as conservation of momentum would seem to dictate? It sounds like it would work essentially like a time-reversed rocket engine (high energy particles going in instead of out, excess energy going out instead of in), which suggests there'll be an equal and opposite reaction to worry about.

Suppose the projectiles are 1% the mass of the receiver station, M_S. Suppose the station is floating stationary in space for simplicity, and suppose we use the figure of 78.6 km/s for projectile velocity. Total momentum before capture is:

• P = M * V = 0.01 * M_S * 78.6 km/s = 786 m/s * M_S

Capture (via whatever means) effectively transfers that momentum to the station; afterwards, the station-pellet system goes from a standing stop to velocity:

• V = P / M = (786 m/s * M_S) / (1.01 * M_S) = 778 m/s

... which is about 10% of LEO velocity. To keep the station in the same orbit, you'd need to perform a burn of that magnitude to compensate, per projectile. And since it's an orbit, I don't think catching another pellet can do the job; assuming they all approach from the same local direction, you'd be raising apoapsis on one side of your orbit and lowering periapsis on the other.

I initially answered this with a bunch of math for cost, but after almost finishing, I realized alternating receiving slugs between the side of the orbit which would accelerate the receiver station and the side which would decelerate it would lose some of the energy, but require zero fuel. I kept the math for if it was always decelerating anyway:

So if the figure from the OP of 1.729 GJ/kg is right, and the cost per joule from here of 2.8 * 10^-8 $/joule ($28/GJ), each kilogram coming in is worth $48.412 USD, assuming no losses in recovery. According to this, mass driver efficiency is about 50% with current technology, and my understanding is that that's the same whether you're launching or decelerating. So each incoming kg is worth $24.26 USD, minus 15.7 MJ/kg for launch = 31.4 MJ for efficiency losses = $0.8792 USD is $23.3808 USD profit, per kilogram. So that means if you have a 1 ton station (which seems on the light side for something like this) every time you need to boost the station by that much, you've made $233.81 USD. With a specific impulse of 450 s, you'd need to launch 193 kg of fuel from earth. so with current $/kg to orbit this would be impossible, however if fuel was transported from the asteroid belt, with reusable tugs, this could easily be possible with existing technology. SSTO/fully reusable rockets might be able to get the cost down to $1/kg to orbit someday too. Using NTRs with Isp's of 900 s would drop the fuel requirements to 92 kg, however ion engines would probably have too low of a thrust to counteract the stream of slugs. Interestingly, it appears that adding or removing mass from the station would not actually make a difference. If it was ten times heavier, it would be affected 1/10 as much, but need 10 times more fuel.

7 minutes ago, YNM said:

Also, there's one basic question :

If the sending and receiving bodies are different, doesn't that just mean you've moved the energy generation somewhere else ?

This isn't "free energy", this is just a transmission line. In the wrong direction.

I think it it essentially the oberth effect. Mass just has more energy the lower it is in a gravity well.

[YNM]

25 minutes ago, Mad Rocket Scientist said:

I think it it essentially the oberth effect. Mass just has more energy the lower it is in a gravity well.

I could envision a future where we'd want some sort of "transmission cables" between Earth and Mars in the future, but guess where most of the energy flow is going in that.

There's also the question that you can't (absolutely can't) do this from one body to the same body. They'd be in different angles, and there'd be no energy gained.

Edited June 8, 2018 by YNM

[HebaruSan]

53 minutes ago, Mad Rocket Scientist said:

With a specific impulse of 450 s, you'd need to launch 193 kg of fuel from earth. so with current $/kg to orbit this would be impossible, however if fuel was transported from the asteroid belt, with reusable tugs, this could easily be possible with existing technology. SSTO/fully reusable rockets might be able to get the cost down to $1/kg to orbit someday too. Using NTRs with Isp's of 900 s would drop the fuel requirements to 92 kg

Very interesting. You led me to another point of analysis...

Suppose very generously that we have a 10 km long capture station, and suppose capture takes place as the projectile travels along that 10 km span. Assuming constant deceleration, the stopping time for a slug traveling at 78.6 km/s over a 10 km span is:

• t = d / v_avg = 10 km / (0.5 * 78.6 km/s) = 0.25 seconds

So the station experiences an acceleration of:

• a = (v₁-v₀) / (t₁-t₀) = (778 m/s) / (0.25 s) = 3112 m/s² = 317 gees

Do we have (or know of) materials that can withstand that?

Edited June 8, 2018 by HebaruSan

[Bill Phil]

5 minutes ago, HebaruSan said:

Very interesting. You led me to another point of analysis...

Suppose very generously that we have a 10 km long capture station, and suppose capture takes place as the projectile travels along that 10 km span. Assuming constant deceleration, the stopping time for a slug traveling at 78.6 km/s over a 10 km span is:

• t = d / v_avg = 10 km / (0.5 * 78.6 km/s) = 0.25 seconds

So the station experiences an acceleration of:

• a = (v₁-v₀) / (t₁-t₀) = (778 m/s) / (0.25 s) = 3112 m/s² = 317 gees

Do we have (or know of) materials that can withstand that?

The acceleration the station experiences is a function of force and mass. Action reaction. If the station is sufficiently massive the acceleration on the station will be far less.

Better question: can asteroids survive that acceleration? If not (and I'm quite sure they can't survive that), you'd need special slugs designed specifically for this purpose.

[HebaruSan]

1 minute ago, Bill Phil said:

The acceleration the station experiences is a function of force and mass. Action reaction.

Sure, if those are known quantities, but in this case they're not. It's also a function of change in velocity and duration, both of which are known.

[Bill Phil]

7 minutes ago, HebaruSan said:

Sure, if those are known quantities, but in this case they're not. It's also a function of change in velocity and duration, both of which are known.

The station doesn't experience the same acceleration as the payload, though.

[HebaruSan]

8 minutes ago, Bill Phil said:

The station doesn't experience the same acceleration as the payload, though.

Correct, the payload's acceleration would be much higher than what I calculated above:

• a = (v₁-v₀) / (t₁-t₀) = (78.6 km/s) / (0.25 s) = 314,400 m/s² = 32,048 gees

[FleshJeb]

On 6/8/2018 at 1:04 PM, HebaruSan said:

Correct, the payload's acceleration would be much higher than what I calculated above:

• a = (v₁-v₀) / (t₁-t₀) = (78.6 km/s) / (0.25 s) = 314,400 m/s² = 32,048 gees

The projectiles better be "dumb" then. Guidance could be accomplished by making them reflective and using lasers. The question being, could they have enough surface area while retaining the necessary strength? How much laser energy do you need to pour into them, and would they survive the heating?

How much wider does the laser beam have to be than the projectile? What magnitude of energy losses are we incurring that way?

On another note, I'm assuming this all requires superconductors. Not only for the mass-drivers, but you'd need to store the incoming energy as a magnetic field in a superconducting ring. Any other conductor would get vaporized into plasma.

Hmm, could we do our station-keeping by mag-sailing the Earth's magnetic field?

[kerbiloid]

Why at all bother with catching, when we have a useless Venus?
A place where things can't get worse.

Let the pieces of matter fall into the thick gas and heat the Venus making it hotter, and its atmosphere thicker.
Ejecta will be stopped with the gas drag and stay on Venus. Just its chemically neutral atmosphere will be looking like a boiling gas  ocean.

Collect Venus IR with orbital IR collectors and retranslate.

Sometimes we will get a hot Suburanus.

Also it's a natural place to drop radioactive wastes.

Spoiler

Just don't let Riddick get to there.

 

Edited June 12, 2018 by kerbiloid

[MatterBeam]

On 6/8/2018 at 8:33 PM, HebaruSan said:

Very interesting. You led me to another point of analysis...

Suppose very generously that we have a 10 km long capture station, and suppose capture takes place as the projectile travels along that 10 km span. Assuming constant deceleration, the stopping time for a slug traveling at 78.6 km/s over a 10 km span is:

• t = d / v_avg = 10 km / (0.5 * 78.6 km/s) = 0.25 seconds

So the station experiences an acceleration of:

• a = (v₁-v₀) / (t₁-t₀) = (778 m/s) / (0.25 s) = 3112 m/s² = 317 gees

Do we have (or know of) materials that can withstand that?

A 1kg projectile at 78.6km/s has 78.6kNm of momentum. 
If it is caught by a station that masses 10,000 tons, then the station will gain 0.00786m/s of velocity. It does so in 0.25 seconds, leading to an acceleration of 0.0314m/s^2 or 3.2 milligees. 

On 6/8/2018 at 8:43 PM, Bill Phil said:

The acceleration the station experiences is a function of force and mass. Action reaction. If the station is sufficiently massive the acceleration on the station will be far less.

Better question: can asteroids survive that acceleration? If not (and I'm quite sure they can't survive that), you'd need special slugs designed specifically for this purpose.

The barrel of the catcher station can be mounted on a suspension that smoothes out the impulse from the projectile. However, a realistic asteroid will be closer to hundreds of thousands to millions of tons in mass, so it would not be needed.

On 6/8/2018 at 9:04 PM, HebaruSan said:

Correct, the payload's acceleration would be much higher than what I calculated above:

• a = (v₁-v₀) / (t₁-t₀) = (78.6 km/s) / (0.25 s) = 314,400 m/s² = 32,048 gees

Excalibur artillery shells are designed to survive 40,000g+, despite having complex inertial and laser guidance systems. 

On 6/12/2018 at 1:38 AM, FleshJeb said:

The projectiles better be "dumb" then. Guidance could be accomplished by making them reflective and using lasers. The question being, could they have enough surface area while retaining the necessary strength? How much laser energy do you need to pour into them, and would they survive the heating?

How much wider does the laser beam have to be than the projectile? What magnitude of energy losses are we incurring that way?

On another note, I'm assuming this all requires superconductors. Not only for the mass-drivers, but you'd need to store the incoming energy as a magnetic field in a superconducting ring. Any other conductor would get vaporized into plasma.

Hmm, could we do our station-keeping by mag-sailing the Earth's magnetic field?

There are no lasers involved at any point. 

On 6/12/2018 at 5:38 AM, kerbiloid said:

Why at all bother with catching, when we have a useless Venus?
A place where things can't get worse.

Let the pieces of matter fall into the thick gas and heat the Venus making it hotter, and its atmosphere thicker.
Ejecta will be stopped with the gas drag and stay on Venus. Just its chemically neutral atmosphere will be looking like a boiling gas  ocean.

Collect Venus IR with orbital IR collectors and retranslate.

Sometimes we will get a hot Suburanus.

Also it's a natural place to drop radioactive wastes.

  Hide contents

Just don't let Riddick get to there.

 

You catch the projectiles to turn their kinetic energy into useful electricity. Dumping them on Venus does not benefit anyone. 

[kerbiloid]

8 minutes ago, MatterBeam said:

You catch the projectiles to turn their kinetic energy into useful electricity. Dumping them on Venus does not benefit anyone. 

It would be somewhat tricky to catch the projectiles, while hitting continuously snowing into Venusian clouds (form Oort cloud, at ~70 km/s speed) you could warm it up to, say 1000 K, and collect its IR emission, beaming it to other places.

Its dense atmosphere would be like bags with sand safely catching bullets.

Edited June 16, 2018 by kerbiloid

[MatterBeam]

38 minutes ago, kerbiloid said:

It would be somewhat tricky to catch the projectiles, while hitting continuously snowing into Venusian clouds (form Oort cloud, at ~70 km/s speed) you could warm it up to, say 1000 K, and collect its IR emission, beaming it to other places.

Its dense atmosphere would be like bags with sand safely catching bullets.

Venus's atmosphere is 4.8*10^20kg in mass. It is made mainly of CO2, which has a heat capacity of 850J/kg/K. 

Dropping a one ton (1000x1kg) mass stream at 70km/s into it would heat it up by roughly six trillionth of a degree Celsius. 

Edited June 16, 2018 by MatterBeam

[kerbiloid]

1 hour ago, MatterBeam said:

Dropping a one ton (1000x1kg) mass stream at 70km/s

would give 1000 * 70000² / 2 = 2.45*10¹² J.

2.45*10¹² / 1370 / 86400 = 20700 m² = 140x140 m ideal solar panel near the Earth would give per day.
Or 
2.45*10¹² / 10⁹ / 4 / 60 = Chernobyl power station was giving per 10 minutes when it had 4 reactors running.

So, there would be a lot of 1 t stones to be caught.

Just this solution is for another scale.

We (presumably) have the Oort cloud around the Solar System, from 2000 (inner) to 100000 (outer) AU .
It consists (if exists) of, according to wiki, 5 Earth masses of useless snowballs = 5 * 6*10²⁴ = 3*10²⁵ kg.

Most of them  are in the outer cloud. Say, at 70 000 AU from Sun = 70000 * 1.5*10¹¹ = 1.05*10¹⁶ m.

GM = 2*10³⁰ * 6.67*10^-11 = 1.334*10²⁰ hm... units.

Orbital speed = sqrt(1.334*10²⁰ / 1.05*10¹⁶) = 113 m/s.

***

Say, we are going to drop them all onto Venus (it's a hopelessly dead rock, we can't harm it) or onto Jupiter (it's big, we can't harm it).

Say, collision roughly estimated speed would be at near-escape speed for both planet and planet orbit.
I.e
 ~35*1.4 + 7.3*1.4 ~ 59 km/s for Venus
 ~13*1.4 + 42*1.4 ~ 77 km/s for Jupiter
I.e. ~70 km/s.

Total released energy = 3*10²⁵ * 70000²/2 = 7.35*10³⁴ J.

This is Sun total radiated energy for 7.35*10³⁴ / 3.86*10²⁶ / 86400 / 365.2422 = 6 years
Not so much compared to a Dyson sphere, but much, much more realistic.

To deorbit them we have to apply delta-V ~113 m/s.
Energy got/spent ratio = (70000 / 113)² = 384000 times.
Total deorbit energy = 3*10²⁵ * 113²/2 = 2*10²⁹ J.
So, energetically it makes sense.

Of course, their fight will take time. Several thousand years for the closest ones, up to millions for farther ones.
But why hurry, especially when there is the only enough heavy but easy to deorbit object around..
Also with such energy ration we can spend 100 times more energy and push the comet down, at, say, 1 km/s speed.
Then its flight will last just for ~300 000 years. With total deorbit energy ~= 2*10³¹ J.

Required average power = 2*10³¹ / (300000 * 365.2422 * 86400)  = 2.1*10¹⁸ W.

Say, we have a swarm of light collectors in 0.1 AU near-Sun orbit.
Total area = 2.1*10¹⁸ / 1370 * 0.1² = 15*10¹² m² = 15 * 10⁶ km² of thin collecting mirrors.
Say, 30 mln km2 as a half of them will be behind the Sun or at sharp angle.

Say, 100 mln km² for losses.
Like a 10 000 x 10 000 km sheet.
Sun radius is 700 000 km.

If a million years is appropriate, the mirror can be even smaller.

Edited June 16, 2018 by kerbiloid

[mrfox]

Mathamatically its a momentum exchange tether in reverse. Similar to what is described here -

https://www.google.com/url?q=http://scholar.google.com/scholar_url%3Furl%3Dhttps://arc.aiaa.org/doi/pdf/10.2514/1.44873%26hl%3Den%26sa%3DX%26scisig%3DAAGBfm2VpLOITVrFPGnL9pQmXMIEjv9YTQ%26nossl%3D1%26oi%3Dscholarr&sa=U&ved=0ahUKEwi2656I19rbAhVl6oMKHWy8BosQgAMICygA&usg=AOvVaw3KSueYLqXEqnt0gjQjnV6O

The structural requirements to intercept inbound objects at interplantery speeds would be substantial. Hopefully by that point in our evolution we have figured out better power sources - analogous to how modern solar panels have taken the place of mercury boilers in early sci-fi.