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If the sun's gravity is strong enough to pull a comet from the kuiper belt why does it not pull the planets into it?

I was told that the sun's gravitational pull is so strong that it pulls comets in from the kuiper belt, but why does it not do the same to the planets? Since a comet is so small in size ,mass and density and so far out how is this possible? An old teacher of mine said it has to do with the planets speed and its own gravity, but doesn't a comet move at a faster speed than the planets? Does the fact that comets do not have a gravitational field play into this? Or am I being mislead? This may be a basic question but I have not found an answer that explains this. This question and a few others is making me think I need to take astrophysics in college . Thank you.

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    Nov 18 2012: Alexander,

    A comet's speed in the Kuiper belt is not faster than a planet. The further an object is from the sun, the slower it moves in its orbit.

    If something redirects the comet's direction toward the sun, the sun's gravity will take it over. As it gets closer to the sun, its speed increases due to the force of gravity. As it departs away from the sun, its speed decreases the further it gets.

    Comets do have a gravitational field. Gravity is a function of mass. Everything has gravity including you, otherwise, you would not be held down to the earth. the earth's gravity interacts with your gravity to create an attraction.

    Try an experiment; take a small ball at the end of an elastic and spin it around your head. The elastic is pulling the ball in, but the speed of the ball is pulling it away. Gravity is like an elastic, only it gets weaker as distance increases. But the principle is still the same. The speed of the planets keeps them from falling into the sun. If they were to slow down, the sun's gravity would pull them closer to the sun. It doesn't take much to change the direction or speed of a comet. It would take an enormous force to change the speed or direction of a planet, which is why comets get pulled in but planets don't.

    Simple arithmetic; The earth is 93 million miles from the sun. It takes 365.25 days to go around the sun. Circumference is 3.1416 times diameter. How fast is the earth moving?
    The moon is 240,000 miles from the earth (rough estimate). It takes 29.5 days to go around the earth. How fast is the moon moving?
    When you calculate it out, it becomes surprising at just how fast celestial objects move through space.

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