He also found the four moons of Jupiter. This is important because objects that are orbiting Jupiter cannot also be orbiting the Earth, and therefore the geocentric model is not likely to be true. Weight is a force. It is the force of gravity pulling on a mass at the surface of a planet. A person's mass will not depend on that person's location.
Weight is equal to mass times the acceleration due to gravity at a given location.
The sidereal day is 3.9 minutes less than the solar day. Seasons are caused by the tilt of the Earth's rotation axis with respect to the ecliptic. Also, the new Moon is not visible because the sunlit portion of the Moon is facing away from the Earth. They were based on Tycho Brahe's observations. The laws also hold true for any two objects in orbit around each other due to gravity.