Can we change Earth's orbit with modern technology? [closed]

Question

It is well known that, according to Newton's 3rd law, spacecrafts entering or leaving Earth provoke tiny (insignificant) changes to Earth's orbit (see related question here).

My question is about significant changes. For instance, say we would like to shift the Earth's orbit closer to that of Mars (forget about the ecological consequences of this). Do we currently have the technology capable of doing this? For instance, something like a huge nuclear explosion? This question only deals with "natural", non-human ways to change a planet's orbit. I am interested about technology-based changes.

Answer 1

No, we cannot.

It's relatively simple math to show that we are a very long shot from changing Earth's orbit by anything significant at all: consider the kinetic energy of Earth in its current orbit, and do the same math for that in the desired orbit:

$ E_{kin} = \frac{m_E}{2}v^2 \approx \frac{m_E}{2}\frac{GM_S}{a}$

where $m_E = 6\cdot 10^{24}$kg is Earth's mass, $M_S=2\cdot 10^{30}$kg is the solar mass and $a=150\cdot 10^9$m is the distance from Earth to sun. I used the approximation in calculating orbital velocity $v = \sqrt{\frac{GM_S}{a}}$ that the Earth mass, is much smaller than the Sun's mass. So current orbital velocity is (using numbers as above) $29822$m/s.

Now, changing oribital distance outward by 1%, thus by $1.5\cdot 10^9$m, to $151.5\cdot 10^9$m yields a speed of $29674$m/s - and in energy that subsequently gives a difference of $2.64\cdot 10^{31}$J to move Earth's orbit about 1% to further from the Sun.

Annual world primary energy production currently is around $10^{20}$J - so we "just" need to produce 100.000.000.000 times the yearly energy production of the entire world to change Earth's orbit about 1%. And that implies that we have a technique to transfer energy 100% into Earth orbital velocity - something which cannot exist either due to simple thermodynamic argument.

Edit to add: Another way to argue is the rocket way: typical speed of conventional rocket exhausts are a few km/s, which is less than needed to leave Earth's orbit - that's why you need multi-stage rockets to get anything into orbit. But if you want to move the whole Earth with a rocket motor, you need a propellant which is fast enough that it directly leaves Earth's gravitational field - or you will not be able to create any effective change of momentum and only move around mass in the Earth system itself. So you need to make some substantial technological advances here, too - or some entirely different technique.

Answer 2

I'll go out on a speculative limb and say yes, maybe, depending on the definition of "significant".

Planetmaker's answer notes the infeasibility of raising Earth's orbit if nothing else changes. But what if we also lower some other body's orbit at the same time?

First, let the orbital energy of an object with mass $m$ orbiting the Sun with mass $M_S$ at an average distance of $a$ be its kinetic plus potential energy with respect to the Sun:

$E_k + U = \frac{1}{2}m v^2 - \frac{G M_S m}{a} = \frac{1}{2} m (\sqrt{\frac{GM_S}{a}})^2 = \frac{G M_S m}{2a} - \frac{G M_S m}{a} = -\frac{G M_S m}{2a} $

Our goal is to raise the Earth's average orbital radius by 1%. Using the above equation and the specific values listed at the end, we need $2.62 \times 10^{31} \ \mathrm{J}$ to do that. (This is all consistent with planetmaker's calculation, I just want to show my own work.)

Where can we get this energy? Let's try stealing Ceres. If we drop its orbital radius down to match Earth's, we gain $2.65 \times 10^{29} \ \mathrm{J}$. That's only 1% of the required energy. But if we instead are content to change Earth's orbit by 0.01% (is that "significant"?) then we have enough energy to do it in Ceres. If not, we need to get more bodies involved. (Since Ceres alone is already about 30% of the asteroid belt mass, they will need to come from elsewhere.)

How do we transfer energy from Ceres to Earth? We arrange for a series (no pun intended) of Gravitational slingshots between the two bodies, each time letting Ceres pass just ahead of the Earth, thereby transferring energy to the latter. (As an outline of the encounter plan, my basic idea is we start by lowering its periapsis to match Earth, then all encounters happen at Ceres periapsis, thus preserving the possibility of future encounters.)

How do we change the orbit of Ceres to cause these slingshots? We apply the same technique, recursively if needed. Find something else nearby, presumably also in the asteroid belt, whose orbit we can perturb to cause encounters with Ceres, gradually steering it toward the eventual encounter with Earth. The bottom of the recursion is some object small enough to be pushed (perhaps slowly) into an encounter with the next object using existing spacecraft and propulsion technology.

This would of course take a long time, at least tens to hundreds of thousands of years, but still well short of the hundred billion years planetmaker cited to move Earth using terrestrial energy sources.

At the core of this idea is the observation that N-body gravitational systems are chaotic, meaning that small changes in initial conditions can cause very large changes in later system state. To move the world, Archimedes asked for a lever and a fulcrum. But with modest technology, accurate foresight, and ample patience, in principle we should be able to manipulate the solar system almost at will without either.

The Wikipedia Asteroid capture article discusses some related concepts.

Specific numbers used in calculations (generally taken from Wikipedia):

• $G = 6.67 \times 10^{-11} \frac{\mathrm{m}^3}{\mathrm{kg} \ \mathrm{s}^2}$
• $M_S = 1.99 \times 10^{30} \ \mathrm{kg}$
• $m_\mathrm{Earth} = 5.97 \times 10^{24} \ \mathrm{kg}$
• $a_\mathrm{Earth} = 150 \times 10^9 \ \mathrm{m}$
• $m_\mathrm{Ceres} = 2.38 \times 10^{20} \ \mathrm{kg}$
• $a_\mathrm{Ceres} = 414 \times 10^9 \ \mathrm{m}$