Could Passing Asteroids Alter Milanković Cycles and Trigger Climate Change?

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TL;DR
What phenomena could possibly affect Milanković cycles?
Our planet being smacked by a huge asteroid is a common doomsday trope. But what if our planet didn't actually get smacked but came close to getting smacked? Could a sufficiently large body, or perhaps a group of several large bodies, pass close enough to alter the workings of the Milanković cycles such that our planet might go into a premature ice age or heat up enough to melt the polar ice caps for good? Are there any other theoretical phenomena that could accomplish the same?
 
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Earth is big compared to every object that could realistically make a close fly-by.

Chiron with a diameter of ~200 km is the largest object in a very unstable orbit. It has a non-zero chance to make a close fly-by at Earth in the next few million years. It has less than 1/100,000 of Earth's mass. An ideal close fly-by could potentially change Earth's velocity by ~0.1 m/s, changing the mean distance to the Sun by up to 1 part in 300,000 and changing the equilibrium temperature by something like 0.001 K (all orders of magnitude estimates). The global average temperature is currently rising by ~0.2 K per decade, so this is of the same scale as one month of global warming in either direction - and even that needs extremely unlikely conditions to happen.
Gulfton said:
that our planet might go into a premature ice age or heat up enough to melt the polar ice caps for good? Are there any other theoretical phenomena that could accomplish the same?
Humans are working on the ice caps...
 
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Appreciate the detailed response. I was aware that the known bodies that could possibly give us a close call are relatively small; you show that even a small body like Chiron could tweak things, albeit just a wee bit. I would assume then that larger bodies would do considerably more tweaking. Think of something the size of our moon, or maybe even a couple of bodies that big, traveling in tandem. Or even bigger bodies. Would it be safe to assume that IF such a thing were to happen that it would have a dramatic effect on the Milanković cycles? (If you take this and run with it, you might be able to pitch it to Hollywood as the plot for a blockbuster disaster movie.)
 
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