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The prime force that keeps a planet's orbit around the sun is called "gravity".
There seems to be an attraction between molecules and bodies in free space.
If these bodies possessed no existing momentum in some other direction ... in other words, if these bodies were more or less 'still' in space (which they are not - all things are in motion) ... but if they were still, they would immediately commence moving towards one another. As gravity is a Force, and forces possess an acceleration component, their attraction towards one another would pick up speed indefinitely - moving ever faster until they collided with one another with quite some impact.
The size or "mass", specifically, of a body also determines the force of gravity which it exerts on other objects.
But as bodies are naturally all moving in a direction within space, there exists some interplay between their mass, their existing direction of movement and the force of attraction that exists between these bodies in question.

It seems, however, that design is such that bodies are moving in a set path. They seem to be in position such that their natural momentum in space is just sufficiently 'reigned in' enough by the gravity or the attraction that exists between these bodies that they are maintained in some perceptibly 'fixed' orbit around the sun. Of course, in addition to the sun, there are other moving bodies and forces out there which are also involved and which also exert some influence upon the orbit of any one planet and cause an interplay which affects the whole system generally: it is not merely a fact of the dual relationship between just the planet and sun. The many other objects in existence all carry their effect as well. There exists quite a complexity of involvement between all bodies.
Neither is it merely 2-dimensional, as we are often wont to imagine. Many bodies revolve at various angles to the planes at which other bodies and planets move in space! Some move in an orbit that almost meets at a perpendicular to most of the system.

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Q: What force keeps all the in orbit around the sun?
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The Sun's strong gravity keeps all the planets in orbit around it.


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