What would it take to move the Earth out of its orbit?

Question

According to wikipedia, the Earth orbits the sun at an average distance of 149.60 million km.Say we wanted to move the Earth slightly outside its current orbit so that its average distance from the sun was a full 150 million km.What would that take?In particular: would a collision with something really big, like the moon, or a dwarf planet, do it? How big would "big" have to be (say, in Earth masses)? Would the moon do it?How about if a huge mass magically materialised on the surface of the Earth? Would that somehow knock the Earth out of orbit? If so, how big would that mass have to be?I'm sorry but I can't reveal the real motivation behind my question. I am definitely not planning to build a doomsday device so that I can rule the world.(Seriously, I'm just wondering and I'm not a physics geek so I don't know how to start thinking about this).

FiatLuxDave · Accepted Answer

Here is a relevant paper which may answer some of your questions: https://arxiv.org/abs/astro-ph/0102126I've been slowly writing a paper about how to move planets by using repeated gravitational assists from masses moving in orbits which repeatedly cycle between inner and outer planets, conveying momentum from one planet to another. Unfortunately, I just don't have time to finish it right now. Feel free to email me if you want to discuss this stuff in more depth.

ColinWright · Answer

You'd need an injection of delta-vee to move to an elliptical orbit where perihelion is the current distance, and aphelion is the desired distance. So you need to accelerate the Earth by some amount. When it gets to aphelion it's not moving fast enough to stay there, so you need another injection of delta-vee to increase the speed to maintain the new orbit. Note that the new speed in orbit is less than the old speed, despite adding speed twice, because the Earth will lost speed as it climbs up the gravity well.
Then you remember that Kepler's law is R^3 is proportional to P^2, where R is the distance and P is the period. So you can compute the new P based on the old P, and start doing sums from there.
Could probably be done on the back of an envelope with a little more work, but I'm not in a position to do so now. If you're serious, get no better answer, and can wait a day or two, email me.

antstrangler · Answer

You have to add velocity to the earth along it's orbit to raise it.
Would the moon do it: Size does not matter (despite what my ex may tell you). You can accelerate a bowling ball by throwing a tennis ball at it hard enough. You can do the same with the earth and moon if you throw it hard enough.
Lets give it a whack to increase perihelios by 0.89M km so that we average 150M km and a more circular orbit. We'll need a velocity increase of about 0.33 km/s. If we assume that it's an inelastic collision we'd need to throw the moon at the earth at about 27km/s.
It's popular to measure energy in comparison to nuclear weapons. That is about 10E14 times the energy of the most powerful nuclear bomb ever designed.
You should dobule check my calculations before sending out RFQ for your doomsday device. If you just send this out to a contractor you will run the risk of looking silly to people who know what they're doing.

wreet · Answer

As someone who is building a doomsday device I am curious about this too.

Piskvorrr · Answer

I'm pretty sure there's an XKCD what-if on this. Or ought to be.