Ask HN: What would it take to move the Earth out of its orbit?
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).
13 comments
[ 2.5 ms ] story [ 52.2 ms ] threadThen 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.
Equally: "... would a collision with something really big, like the moon, or a dwarf planet, do it?"
As always, it depends on the speed and direction, as much as the mass. But if it happened, I suspect we'd have bigger problems to worry about than what out new orbit would be.
Or no problems at all.
I'm not sure about mantaining the new orbit, rather than falling back towards the sun, as per your comment, but I'm guessing that if the Earth was pulled away from the sun by something as large as another star then it would just start falling towards that other star.
Anyway to be honest I didn't need an exact calculation, more a general intuition. But thanks for the offer :)
OK, so you give it a boost. Assuming you've boosting along the orbital path, it's now travelling exactly in the same direction as it was, but faster. Its new path is an ellipse that rises to a higher peak (aphelion), slowing as it goes, but when it gets there it has lost a lot of speed.
And in fact, it now doesn't have enough speed for that new, higher orbit (even though the speed for that orbit is less than the original), and because it's an ellipse that passes through that original position, it will not stay at this higher altitude, but will trace the second half of the ellipse back to the original position.
The magic term is "Hohmann Transfer":
https://en.wikipedia.org/wiki/Hohmann_transfer_orbit
Again, let me know if you want more, but I see others have made similar offers so I won't be offended if you don't ask.
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.
I'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.