Planetary-Scale Engineering Using Relativistic Hulks

According to special relativity, a container of hot gas, in which individual particles are moving rapidly within the system, will weigh every so slightly more than a container of cold gas. This is because, the faster a mass moves relative to rest, the more mass it has (from it's own frame of reference, there is no change). Objects weigh more in proportion to the fraction of the speed of light, seeming to approach infinity as the fraction approaches unity. See my previous post for tons of mathematical examples of this effect. Cosmic rays, for instance, are lightweight particles (electrons and atomic nuclei) that have been made heavy through acceleration.

I'm going to use this concept as the basis for a mega engineering thought experiment. One of the requirements of this thought experiment is that we have access to unlimited drive energy onboard a starship. There is no known way to achieve this, and no terribly realistic ideas for fixing this particular inconvenience. Therefore, the source of drive energy is in the realm of pure science fiction. The idea described here doesn't work with ram scoops, antimatter rockets, or interstellar lasers driving solar sails. It requires something exotic like stretching and exploiting the zero-point energy gradient, tuning into blackholes via a holographic hack, or blocking gravity in one direction, thereby causing the weight of the unblocked universe to pull the ship toward itself. I won't bother to discuss it any further here, other than to ask that you assume the unassumable before we continue.

Imagine that you have an extra-impossible starship. Imagine also that you can accelerate that ship very close to the speed of light. That ship will rise in mass and exert significant gravitational influence on its surroundings. By accelerating to high relativistic speeds, the mass, and therefore the gravitational influence, will both increase, approaching infinity at around half the rate of the increase in velocity (in other words, you'll never achieve infinite mass through acceleration, ie, going from lower velocity to higher velocity to even higher velocity.)

Imagine if you were to pass by an asteroid, comet, or even a small moon traveling at a high percentage of the speed of light. You could, according to this idea, cause a gravitational pull on the side that the ship passed by. By doing flybys with many heavy fast ships, you could nudge your target off its original orbit. With careful planning, via advanced simulation, you could engage not just in terraforming, but solarforming- the modification of a solar system to make it more inhabitable.

For instance, imagine a planet is already in the right approximate location, but its precession and eccentricity are out of synch, disallowing regular seasons. Using this method, you could flatten the eccentricity by nudging the planet toward its star while at apogee (greatest distance from the center of orbit). You'd do this by passing your ship between the planet and the star. Alternately, you could pass on the the far side while the planet is at perigee. You could also speed or slow the orbit of the planet by passing in front or behind. By using multiple ships and multiple pass-bys, you could fine-tune the orbit.

On the down side, a point mass passing close to a target would exert massive tidal forces. The most powerful effects would also be the most violent. The surface would be more affected than the core, and the overall effect would be like trying to move a pumpkin by hitting it with a sword. Close flybys would affect rotation more than location (useful for changing the length of the day). Really close fly-bys would rip mountains up by their roots and strip away half the atmosphere.

To be most useful, the virtual masses involved would have to be planetary themselves, and be kept at a safe remove. The effect would come and go very quickly- in a matter of seconds- further dampening the effect.

How heavy, and how fast? For example, a "ship" weighing around 8,500kg (a small commercial truck) moving at 0.999999999999999999999999% of the speed of light (impossible) would effectively weigh as much as the earth when measured from the rest frame (~6e+24kg). Flying something like that through our solar system would have a very disturbing effect. It would cause earthquakes, volcanism, tidal waves- literally- and high velocity winds. Better to use it on planets that aren't yet inhabited.

Would this be a practical approach? No!!! It gets more and more practical the less and less realistic it is (ie, with large masses, higher velocities, and greater standoff). It's a thought experiment that assumes that literally unlimited energy for acceleration is available and can be translated into terrifying, unsurvivable amounts of acceleration. However, if you had access to that much energy, there would be much more efficient ways to use it. You could attach a many of these fanciful drives to the planet directly, or you could use their driving principle at a more fundamental level to get the same effect.

The one advantage is that the above technique uses minimal infrastructure- a single starship run by a single advanced autopilot operating on an extremely precise simulation.

But really, building extensive infrastructure shouldn't be a problem if you're moving planets around, right? Come on.

Cut Your Travel Time in Half

There are some aspects of the universe that are exceedingly difficult to imagine properly. For instance, if you were in a spaceship traveling at half the speed of light, and you were to measure the speed of the light you shot out ahead of you, you'd find that it was traveling exactly the speed of light both from your standpoint, and from the standpoint of the stationary observer. This is true for the spacecraft traveling at 99% of the speed of light as well. Special relativity- Einstein's description of the universe in which there are NO special, or privileged reference frames (one's where light doesn't go the speed of light), leaves us with the understanding that in order for this to be the case- in order for light to always travel light speed- other things we consider to be constant get warped and squished and stretched. The rate of the passage of time. The physical dimensions of objects. Mass. Even the very concept of simultaneity.

While it's difficult to imagine, it's not difficult to calculate.

The factor, called gamma, by which we divide the passage of time for the moving reference frame, or multiply for the rest frame, is a simple calculation.

gamma = 1 / ( square root of ( 1 - ( v^2 / c^2 ))

v is velocity expressed as a decimal of the speed of light, c. C, is 1. 1 squared is still 1. So you can disregard that part of the equation. So...

gamma = 1 / square root of (1 - v^2)

And now for some examples:

v/c___________GAMMA__________percent relative to rest frame
0.0___________1________________100%
0.00001_______1.00000000005_____99.99999999995%
0.0001________1.000000005_______99.999999995%
0.001_________1.0000005_________99.9999995%
0.01__________1.00005___________99.99995%
0.1___________1.005_____________99.49874%
0.2___________1.021_____________97.979736%
0.25__________1.033_____________96.82458%
0.3___________1.048_____________95.39392%
0.33333_______1.061_____________94.28090%
0.4___________1.091_____________91.65151%
0.41660_______1.1_______________90.90909%
0.5___________1.155_____________86.60254%
0.55277_______1.2_______________83.33333%
0.6___________1.25______________80%
0.63897_______1.3_______________76.92308%
0.66666_______1.342_____________74.53556%
0.69985_______1.4_______________71.42857%
0.7___________1.40028___________71.41428%
0.74535_______1.5_______________66.66666%
0.75__________1.512_____________66.14378%
0.78062_______1.6_______________62.5%
0.8___________1.666_____________60%
0.80869_______1.7_______________58.82353%
0.83148_______1.8_______________55.55556%
0.85029_______1.9_______________52.63158%
0.8660254038__2________________50%
0.9___________2.294_____________43.58899%
0.91__________2.412_____________41.46082%
0.91652_______2.5_______________40%
0.92__________2.552_____________39.19184%
0.93__________2.721_____________36.75595%
0.94__________2.931_____________34.11744%
0.94281_______3________________33.33333%
0.95__________3.203_____________31.22499%
0.96__________3.571_____________28%
0.96825_______4________________25%
0.97__________4.113_____________24.31049%
0.97980_______5________________20%
0.98__________5.025_____________19.89975%
0.98601_______6________________16.66667%
0.98974_______7________________14.28571%
0.99__________7.089_____________14.10674% (two nines of c)
0.9949874371__10_______________10%
0.999_________22.366____________4.47101% (three nines of c)
0.9999________70.712____________1.41418% (four nines of c)
0.9999499987__100______________1%
0.99999_______223.607___________0.44721% (five nines of c)
0.999999______707.107___________0.14142% (six nines of c)
0.9999994999__1000_____________0.1%
0.9999999_____2236.068__________0.04472% (seven nines of c)
0.99999999____7071.068__________0.01414% (eight nines of c)
0.999999999___22360.680_________0.00447% (nine nines of c)
0.9999999999__70710.678_________0.00141% (ten nines of c)
1.0000000000__(infinite)__________0%

Notice anything interesting happening at high c? Makes it easy to remember, doesn't it?

Let's put gamma to work in some simple operations.

Q. A ship with a 1 gram rest weight is traveling at ten nines of the speed of light. How much does it weigh?

A. 1g x 70710.678 = 70.7kg.

Q. A neutrino with negligible mass is moving exactly the speed of light. How much does it weigh?

A. (almost nothing) x (infinity) = infinite weight. In other words, neutrinos *don't* quite make light speed. Light, which can only travel at light speed, is completely massless.

Q. A one-kilometer long ship is traveling at 0.8c. How long is it when viewed from the rest frame?

A. 1000m x 0.6 = 600m.

Q. A starship is traveling at four nines of the speed of light for ten years according to the rest frame. How many years ass on board the ship?

A. 10 x 0.014142 = 0.14142 years or 51.65 days.

Q. A ship is traveling at 96% of the speed of light for ten years of shipboard time. How many years pass on earth?

A. 1 / 0.28 x 10 = 35.71 years.

Q. At what speed does relativistic time dilation cause shipboard travel time to be exactly half that of the rest frame observer?

A. To find the answer, we set gamma equal to 2 and solve for v.

2 = 1 / square root of ( 1 - v^2)

Divide both sides by (square root of ( 1 - v^2)
Reset.
Divide both sides by two.
Reset. Get 0.5 = square root of ( 1 - v^2)
Square both sides.
Reset. Get 0.25 = 1 - v^2
Subtract 1 from both sides.
Reset. Get -0.75 = -v^2
Take square root of both sides.
Assume the answer we desire is positive.
Get 0.8660254038 c.

v = square root of [ - {(1/gamma)^2 - 1} ]

That's how fast you'd have to travel to cut your travel time in half.