1- what is the scientific/historic significance of Keplers 3rd law? 2- why is th

Question

1- what is the scientific/historic significance of Keplers 3rd law?
2- why is the gravitational potential energy of a satellite negative?
3 - what is geosynchronous satellite?
4' you watch a plane fly horizontally overhead with constant velocity. in what way does its angular momentum change relative to you a stationary observer on the ground? explain your answer.
5- why does an ice skater with their arms extended to their sides, in a spin about a vertical axis, rotate faster when they bring their arms in toward their body?
6- of rotating object experienced a tangential acceration in a direction of rotation, what would happen to the size of the angular velocity? explain your answer.

Explanation / Answer

(1)  Kepler's laws describe the motion of planets around the Sun. Kepler knew 6 planets: Earth, Venus, Mercury, Mars, Jupiter and Saturn. with the help of keplers law, we can easily calculate the period of all the planets. knowing the periods of planets we can calculate the radius of orbit of each planet and we can get its exact position of the planet around the sun.. Additionally, the same law that describes the T2/R3 ratio for the planets' orbits about the sun also accurately describes the T2/R3 ratio for any satellite (whether a moon or a man-made satellite) about any planet. we can also derive newtons law of gravitation from the Keplers third law.

(2) gravitational potential energy of a satellite is always negative. this is because the gravitational forces are always attractive.so there is alway attraction between the panet and satellite.

(3)A geostationary satellite is an earth-orbiting satellite, placed at an altitude of approximately 35,800 kilometers directly over the equator, that revolves in the same direction the earth rotates (west to east). At this altitude, one orbit takes 24 hours, the same length of time as the earth requires to rotate once on its axis. The term geostationary comes from the fact that such a satellite appears nearly stationary in the sky as seen by a ground-based observer

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