Satellite Motion Mathematics

What are the equations used in satellite motion problems? How do you solve all these satellite motion problems? What equation should I use? How do you calculate ... ? And (most importantly) what's Mr. H hiding above his belly button? If these questions and related ones are causing trouble, then give Mr. H 11 minutes of time and trouble no longer.
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Minds On Physics, Mission CG8: Satellite Motion
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Calculator Pad, Circular Motion and Gravitation section, Problems #19-27
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Tutorial on Circular and Satellite Motion; Lesson 4: Mathematics of Satellite Motion
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[@faouzimostefaoui8774]

Thank you!
I've a question:
Is the radius of artificial satelite around earth is constant? Because kepler's first law tell no!
So if radius is not constant speed will not be contant too?!

[@PhysicsclassroomVideos]

Most communication satellites try to keep the R and v as constant as possible. Surveillance satellites tend to have a more elliptical orbit.