Why Satellites don't fall down? Well, technically they fall down soon or later... let me explain...
Newton confirms that they must to fall back to Earth as the apple did on his head.
Newton's Law of Universal Gravitation
As Wikipedia says: Newton's law of universal gravitation states that a particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.
F is the force between the masses;
The idea was to put again a copy paste of the Wikipedia's definition but believe me... it's not a good idea.
Let me try to explain what is the centripetal force. When you run normally you are moving straight foreward.
Now imagine that you run with a hand caught to a lamppost. What happens? you are running as before but a Force (your arm) does not let you get away from the pole. Your arm is the centripetal force. A Satellite is always falling to the Earth. But velocity tries to push it away. The sum of forces is a circular motion.
F is the Centripetal force
m is the mass of the satellite
v is velocity
r is radius. Remember: the distance from the satellite to the centre of the planet, not to the surface.
Of course, if velocity is too fast the satellite will leave Earth's gravity. If it is slower than requested the satellite fall back to Earth.
Surely you see that: Centripetal Force and Gravity are the same force... Yes
We are going to use the next formulas where : first formula Fc is Centripetal Force, msat is Satellite mass, v is velocity of the Satellite, r radius or distance between the centre of the satellite and the centre of Earth, the second one FG is Gravity Force, G is the gravitational formula, ME is the Earth mass, msat and r the same as said before.
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