Is is possible for an object with a small mass to have an orbit?
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Yes, small mass can orbit in space.
An example would be small asteroids, ice, and dust and other meteor fragments..
So it's possible... In space only? Like, is it possible on Earth too? Or does gravity prevent that?
Nothing really orbits in earth.
Only around earth.
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The Sun and Moon is not on the earth but it faces it.
A body can orbit round the earth at a certain distance...say where yhe moon is present even an apple would be that far it will orbit round the earth..
That may also depend on how small the mass is. if it is one atom of helium then it will eventually slow down faster then one with more mass in orbit but it may be able to be at the edge of our atmosphere.(even space is not a complete vacume). small flecks of paint and debree are orbiting space right now and they are very dangarous becausse of how fast they are moving. Nasa is working on micro rokets that are already orbiting the earth.
so no matter how igh or low you are, as long as you are not touching the ground and there is no opposing force on the object, one may theoreticaly be able to set any object into orbit as long as it has a large enough 'initial velocity'
You can find out this velocity using the equation; Vorbit = √ GM/R