how does a object stay in stable orbit around another object like our sun and earth?

The Earth is indeed falling into the Sun. But it is moving so quickly past the Sun that it continually misses hitting it.

This is not an analogy but one correct way of viewing orbiting bodies.

On a human time scale the Earth's orbit seems stable, but it is not, nor is that of any other planet. The Earth's orbit is elliptical and the distance to the Sun changes constantly and so does Earth's orbital speed.

The Earth's average annual distance from the Sun also changes. Several of our solar system's planets were in quite different orbital locations millions of years ago.

The gravitational interactions of the planets constantly changes their orbital characteristics. Sometimes this causes a planet to get ejected from the system and into deep space. We don't know how many times that has occurred in our solar system.

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If there were only two objects in the universe they could orbit their mutual center of gravity in a relatively stable configuration. But in the real universe, every object with mass has gravity and affects all orbits.

The ISS orbits the earth, but experiences atmospheric drag which has to be corrected. A planet in orbit around the sun doesn't have any substantial drag to deal with which makes the orbit more stable. The Vanguard 1 satellite which orbits higher than the ISS was launched in 1958 and is still in orbit. Once a certain velocity is achieved the object will remain in orbit unless acted upon by other forces like drag. The earth's low elevation orbital velocity is about 18000 mph.

Im only in 10th grade so don't get mad if I get this wrong but I believe it's because of the gravitational pull of a large objects such as the Sun keeping it in place, Newton's laws, and in space when an object moves it will not stop until another force stops it or goes against it so when it is set in motion it keeps on going. And the earth constant movement swing around the Sun I suppose would be throwing us away from the Sun just as much as it's pulling us in.

The force of gravity pulling the object towards the central axis is balanced by the objects momentum traveling at a 90° angle away from the central axis.

This is the same thing that happens when you spin a weight on a string in circles.

The string is a depiction of the force of tension, which is doing the exact same thing gravity does for an orbiting planetary body.

I left a very good link on the subject in the source :)

In my understanding, since it's a rotating reference frame (in this case the gravity of the sun plays the role in keeping other planets orbit around it), there must be an equal opposing force to that gravity. If you view the sun-planets system as a non-inertial reference frame, then the inertial centrifugal force should be the one that balances the gravity force.

Hope it helps:D

because with the rotation around, the force exerts outward at the same force that gravity pulls. Essentially think of a ball tied to a rope and u swing it around ur head. Their is force in the rope that is keeping the ball in place equal to the outward force the ball is exerting. Now when u let go the ball flies away which would be like if gravity suddenly stopped. Essentially the earth is a ball on the suns gravity string

they stay stable because the centripetal force pushes the planets away while the sun's gravity pulls it in, the two forces balence each other out creating stable orbit.