Please provide a mathematical example with a solution. showing all the work, and ultimately, answer the question. Some questions might answer multiple questions in this document. While you can use the same question more than once, you will need to re explain how it adresses $$ Question $1.$ Why is the acceleration of uniform circular motion directed toward the centre of a circle? $2.$ Using circular motion to approximate elliptical orbits, how can you describe the motion of planets, moons natural satellites and satellites artificial satellites $$ using mathematical relationships formulas $3.$ How was Newton able to use Kepler laws that described the motion of planets as elliptical orbits around the sun, to develop his law of universal gravitation? $4.$ What is the relationship between the kinetic energy due to motion $$ the potential energy stored and the total mechanical energy of an object in a closed isolated system? $5.$ What is work? $6$How does the mechanical energy change in a system that is not isolated? $7$ What is power and how does it relate to work?