# Humanity’s first effort at moving a planet

What technology will humanity use the first time it moves a planet?

In the near-ish future, humanity has colonized Mars which has since become self-sustaining and independent, as well as various other solar system bodies. The asteroid belt is a principal source of resources, and a mature infrastructure exists for prospecting and mining, and of course delivering materials to colonies where they are consumed.

In a treaty that seeks not just to redraw lines on a map but reshape the map itself, the King of Ceres has formed a union with the Federated Republics of Mars, and this is to include physically relocating Dwarf Planet Ceres to become Mars' Moon!

This is politically brilliant, as the rest of the Belt, rather than being sore at the loss of a major piece of territory, is more excited about how much money they will make from contracts related to humanity's first megaproject.

The orbit injection must occur within 30 years (but shaping of the orbit may continue beyond that time).

How might this be accomplished? What technology (available to the described civilization) could be used? Please broadly describe the way the plan would work out.

The specific engine technologies available to them is the answerer’s choice. It should be something forseeable today as real science without breakthrough physics. (So, no emdrive, no anti-gravity, no telekinesis, no negative matter.)

This post is the result of this lesson.

See also: The energy requirement of changing planets’ orbits has been discussed previously.

Here are some rocket engines, with numbers, food for thought and common vocabulary. However, don’t limit yourself to only rockets!

• Rockets seem the only option, a lot of them, but could have basically unlimited fuel if you could use whats on Ceres already May 8 '17 at 4:46
• @Kilisi well, I don’t expect them to get out and push! But “rocket” describes a large number of possible technologies. Even things like the gravitational tether used with a rocket shows this isn’t the whole story. May 8 '17 at 4:52
• Do note that Ceres has an orbital inclination of 10.593° to the ecliptic, while Mars' corresponding value is 1.850°, both according to their respective Wikipedia articles (see the sidebar under orbital characteristics). The difference of 8.743° amounts to a possible significant plane change, depending on exactly how you choose the transfer orbit and target orbital parameters.
– user
May 8 '17 at 5:50
• @YehudaShapira no doubt they will call it Project Archimedes. Certainly that would be the title of the book! δῶς μοι πᾶ στῶ καὶ τὰν γᾶν κινάσω! May 8 '17 at 15:05
• @YehudaShapira I do that every time I get out of bed. The place to stand in my bed room floor. The lever is my legs. I wiggle the Earth every morning. Didn't you notice? Well, sometimes I sleep in. May 9 '17 at 2:04

Hoo boy. This is one serious orbital mechanics problem.

The most energy-efficient method of getting a spacecraft (or, in this case, an asteroid) from one roughly-circular orbit into another is with a Hohmann transfer. For moving Ceres into Mars's orbit, this will entail firing thrusters on Ceres directly opposing its direction of motion so that its perihelion (its closest approach to the Sun) just touches Mars's orbit, waiting until Ceres reaches that point, then firing the thrusters again to circularize the orbit.

In order to actually have Ceres fall into Mars's orbit, though, the maneuver must be initiated at exactly the right time, so that when Ceres completes its half-of-an-ellipse transfer orbit, Mars will be right there waiting for it. Ceres has an orbital period of 4.60 Earth years, while Mars's year is only 1.8808 Earth years. They line up about every Mars year and a half, and the transfer itself will take less than half of a Ceres year. If there were rockets planted on Ceres' surface right now, that means Ceres could be in orbit around Mars within 8 Earth-years in the worst-case scenario, where the most recent launch window just recently closed. There's plenty of time to prepare.

The most important quantity in orbital mechanics is delta-V, which basically just measures the amount by which your spacecraft (or asteroid) needs to change its speed, which, in turn, determines how much fuel you need, how much that fuel and the engines used to burn it will weigh, how much more fuel you need to move all that fuel around, etc. It's used a bit like how distances are used when traveling around the Earth.

That Wikipedia page gives the delta-V for the Hohmann transfer as follows: $$\Delta v_1 = \sqrt{\frac \mu {r_1}} \left( \sqrt{\frac {2r_2} {r_1+r_2}} - 1 \right)$$ $$\Delta v_2 = \sqrt{\frac \mu {r_2}} \left( 1 - \sqrt{\frac {2r_1} {r_1+r_2}} \right)$$ where $\Delta v_1$ is the delta-V needed to put the asteroid into the transfer orbit, $\Delta v_2$ is the delta-V needed to synch that orbit up with Mars, $\mu$ is the mass of the Sun multiplied by the gravitational constant G, $r_1$ is the radius of Ceres' current orbit, and $r_2$ is the radius of Mars's orbit.

Plugging those equations into Wolfram|Alpha, we get $\Delta v_1$ = 2.814 km/s and $\Delta v_2$ = 3.272 km/s, for a total of 6.086 km/s of delta-V.

That's actually not a whole lot, in astrodynamics terms. It takes more than that to reach low Earth orbit.

But Ceres is big.

It has a mass of 9.393×10$^{20}$ kg, so changing its velocity by 6.086 km/s would require an impulse of 5.76×10$^{24}$ newton-seconds.

In order for a Hohmann transfer to work, the rocket burns at the beginning and end of the maneuver should ideally be instantaneous. This, of course, is impossible without destroying the asteroid and killing everyone on it; but nuclear pulse propulsion is probably about the closest you'll get without going well beyond the near future.

The engineers of Project Orion concluded that a nuclear pulse drive based on their design could potentially reach a specific impulse of up to 100,000 seconds. Specific impulse, by the way, is a measure of the efficiency of a rocket engine. A specific impulse of 100,000 seconds means that a sufficiently-refined Orion drive could support the weight of its own fuel in Earth gravity for about 100,000 seconds.

The amount of fuel actually required to pull off this maneuver can be derived from the infamous Rocket Equation: $$\Delta v = I_{sp} \cdot g \cdot \ln \left(\frac {m + m_p} m\right)$$ where $I_{sp}$ is the specific impulse, $g$ is Earth's gravity, $m$ is the mass of Ceres, in this case, and $m_p$ is the mass of the thermonuclear bombs serving as propellant.

Solving this for $m_p$ gives

$$m_p = m \left(e^{\frac {\Delta v} {I_{sp} \cdot g}} - 1\right)$$

Invoking Wolfram|Alpha once again indicates that you'll need 2.72×10$^{18}$ kg of nuclear weapons to start the transfer orbit, and 3.16×10$^{18}$ kg of them at the end. And that's if you get someone to restock your asteroid-ship with the second batch of nukes midway through.

Plus whatever you'd need to actually get the asteroid into orbit around Mars, which depends on how close you want it to orbit.

Good luck!

• What about hydrogen fusion powered rockers, as opposed to Uranium-based bombs? May 8 '17 at 10:48
• @JDługosz Unless you can show some citation that they would have a higher specific impulse, it doesn't matter. FWIW, contemporary chemical rockets tend to have a specific impulse in the few hundred seconds range.
– user
May 8 '17 at 10:58
• Even though a theoretical Hohmann transfer relies on a instantaneous impulses for simplicity, it's okay to not use instantaneous impulses in Hohmann transfers; you just integrate as a very large number of very very short pulses back-to-back instead. And when you think of it, that's how rockets as we know them work; every molecule of exhaust provides a non-zero amount of thrust, and could in principle be the last to be ejected by the engine.
– user
May 8 '17 at 11:01
• @MichaelKjörling the trick is to know when to make those tiny pulses. If you swing around the Sun between each, you'll lose a lot of time, and if you don't, you lose a little bit of efficiency. If you thrust the whole way from Ceres's original location to Mars, you are not performing a Hohmann transfer, and your fuel efficiency won't be as good as that of. You also need to plan accordingly. May 8 '17 at 11:20
• @JDługosz The problem with gravitational tethers is they provide very little thrust, and thus cannot be used for a Hohmann transfer (which requires an instantaneous delta-V for maximum efficiency). If there's a low-thrust, high-exhaust-velocity ion/plasma/fusion rocket design out there with a specific impulse well over 100k seconds, it'd be very well suited for a gravitational tether- but the math is much more complex and lies well beyond my familiarity. If anyone who knows more about this can do the math, I'd love to see it! May 11 '17 at 2:50

To get an idea of what sort of numbers we're looking at, I figured I'd look at the "big dumb rocket" method: what sort of scale are we looking at to do a straight Hohmann transfer orbit from Ceres to Mars, ignoring the plane-change that Michael Kjörling mentioned in his comment to the question.

I found an online Hohmann Transfer calculator and plugged in the numbers to move an object from Ceres's orbit to Mars's, and got a result of a bit over 6 km/s of delta-V needed. Ceres has a mass of roughly 9.4 × 1020 kg, so we're looking at something like 5.64 × 1024 Ns of impulse needed to get Ceres into the same orbit as Mars. Which is a lot.

The Space Shuttle Solid Rocket Boosters, the largest solid rockets ever launched, burned 500,000 kg of propellant at an ISP of 268 seconds (in vacuum). If we strapped one of those to Ceres pointing straight up and lit it off, we'd get 1.75 × 10−12 $\frac{m}{s}$ delta-V. We'd need something on the order of 3.5 × 1015 SRBs to get the delta-V needed to move Ceres into Mars's orbit.

If you had some mythical rocket engine that could produce an isp of 10,000, you would still need to shove about 6 × 1019 kg of fuel into it. Or if you're allowed to use Ceres itself as fuel, you're going to arrive at Mars with about 5.6 × 1019 kg less of it than you started.

There are almost certainly more creative ways to do this, involving lasers or slingshots past Jupiter or other things like that, but any plan that's going to move almost a sextillion kilograms of dwarf planet around is going to need a lot of energy. And it's going to need to do so very precisely, to prevent Ceres from slamming into Mars or breaking up due to the forces involved. So, I'm not saying it's impossible to move Ceres into Mars's orbit, but I don't think doing so is within the "near future" of humanity unless we make some astounding breakthroughs before then.

Another way of looking at it: Ceres's specific orbital energy is −161.2 MJ/kg. Mars's is −292.8 MJ/kg. Thus, moving Ceres to Mars's orbit requires 131.6 MJ/kg of energy at a minimum. As mentioned earlier, Ceres's mass is about 9.4 × 1020 kg, so a total energy expenditure of roughly 1.237 × 1029 J of energy would be required. The Sun emits about 3.828 × 1026 J/s, so you'd need to harness the entirety of the Sun's output for over five minutes (323.14 s) to move Ceres into its new home.

Congratulations! Your civilization is a Kardashev 2!