eli5 Does gravity act the same for large objects as it does for small objects. So if I were to shrink planet Earth and the moon to say half the size and the distance between them too then would they continue orbiting. Would this also apply if they somehow became much larger?
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Mass and thus density are extremely important when it comes to gravity. You should explain your question better: does the mass shrink/increase with the volume, or not? It really makes all the difference
That depends on what you mean by “large”.
If you mean “diameter”, then changing the diameter but keeping the mass constant won’t change a thing.
If you mean “mass” then yes, changing the mass will change the orbits.
If you kept the masses the same, it would not matter to the orbits of the moons or earth.
But the interesting thing is that how close you can get to the center of mass has extremely severe implications.
The closer you are to the center of mass the more intense you feel the pull of gravity.
In theory, if you magically shrunk all the mass of the earth to smaller than the size of a coin, all that mass would collapse into a black hole, which not even light can escape from. The moon would orbit the same, and it would orbit the same around the sun, but anything that got close to the earth would get ripped to shreds by gravity.
Likewise if you ballooned the earth out and some how managed to keep it structurally sound, you would experience less and less pull.
Yes to your first question, “not quite” to the second. Laws of gravity are the same for big and small object. However, these laws state that the force between objects is proportional to their mass and inversely proportional to their distance squared (distance * distance).
So, they can still orbit each other (any pair of objects in space can orbit each other if their relative speed allows it) but just dividing all sizes in half (unless you mean just compressing the Earth and the Moon while keeping the mass and distance intact) will screw up the equations, so their orbital speeds and parameters of the orbit will be different.
If you look at the equation for calculating the gravitational attraction between two bodies, it depends only on the two masses and the distance between them. The sun could be ten times its current size or could be collapsed into a black hole, and we would orbit it just the same.
We might be personally more or less happy with the living conditions, but a year would still be 365 and a bit days.
What do you mean by “size” and “larger”? Are you talking about radius or mass or both?
Gravity is a function of mass. If you shrunk Earth an the Moon to half their *radii* but kept their masses the same, their orbital dynamics would be the same. If you changed their masses, then their orbital dynamics would change.
Our sun has a radius of about 7000,000km, If you replaced our sun with a black hole with the same mass but a radius of only 1.5km, the planets would continue to orbit the black hole as if nothing had changed, gravitationally speaking.
So, if you double the size you get 8 times more mass, 8 times more gravity.
Distance: if you double the distance you get 1/4 of the gravity.
Double up everything keeping the same scale:
8 mass but 1/4 gravity because distance = doubled attraction between the two.
Now, it works or not depending of moon speed.
Should be: 0,35 of its actual angular speed. So 2.85 times more days to do an orbit, 80 days for an orbit, in a double all dimensions scenario.
The math equation for working our gravitational force only has the following components:
Mass of objects,
Distance,
The gravitational constant.
The constant remains the same. So the only variables are mass and distance.
Gravity affects all mass at all distances.
However, the effect of gravity over vast interstellar and intergalactic and beyond distances is negligible in calculations when figuring out orbits of planets and moons.
For example the black hole at the centre of our galaxy doesn’t noticbly effect the orbit of the moon around the earth. It does have some effect but its so small it isn’t meaningful for human understanding.
There’s actually a cool demo of this in “Universe Sandbox”–it has an example scene of some teacups orbiting a teapot. Works exactly the same as the Moon orbiting the Earth only on a much, much smaller scale.
The short answer is yes, gravity is the same, but the different variables are not always proportionate. So if the masses were cut in half, that doesn’t mean that the distance should be cut in half, or that the 29 day orbit of the moon will still be 29 days or 14.5 days, for that matter These may have to be different.
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