CRASH COURSE PHYSICS EPISODE #1: Universal gravitation No one (including me) really seems to understand physics when Bordak teaches so I decided to translate all the Universal Gravitation stuff to plain English lol. A couple of pointers and things to start with. 1) In the picture shown: a r CB is the radius of the planet. It is what you use when you use r orb is the radius of orbit of an object around planet. This is what you use in Kepler s Law () and when you calculate orbital speed, potential energy, and mechanical energy Remember, F g = m p g =where M is the mass of the central body and where m = m p or the mass of the other object in consideration. So in reality, the when calculate the mass of a central body, the mass of the other object in consideration doesn t matter. you 2. When calculating work and energy of a satellite or whatever IN AN ELLIPTICAL ORBIT : Its initial energy is almost always (in this unit) potential energy () where M the mass of the central body and r is the radius of orbit. When asked to calculate the mechanical energy, assuming the object goes to infinity distance and never comes back, the final kinetic energy changes because the VELOCITY of the object is ZERO at infinity distance Whenever the satellite is doing work on itself, that work is always equal to the total energy of the system (). Whenever something else is doing work on the satellite in orbit, that work always follows the Law of Conservation of Mechanical Energy: E 0 + W = E f The initial energy of any object orbiting a central planet is ALWAYS negative. 3. Eccentricity: Eccentricity only exists for elliptical orbits Eccentricity is equal to the difference of the aphelion and perihelion speeds or distances divided by their sum Maximum speed refers to perihelion speed Minimum speed refers to aphelion speed Escape velocity is minimum velocity needed to get an object in orbit to escape the central body and never
come back ****REMEMBER, ON WEDNESDAY S TEST YOU GET ALL OF THE EQUATIONS!!!!**** 4. Newton s Laws of Motion and Universal Gravitation Since represents a force acting on a set mass, Newton s Second Law applies. So, if there is a force acting on a set mass, that mass must be accelerating! To get that acceleration, as always F = ma! When asked what force an object will exert on another object exerts a force of F on it, the answer is always F at the angle + or - 180 degrees (doesn t matter which) because of Newton s Third Law 5. Orbital Radius vs Altitude vs Radius of Planet It is important to understand the difference between orbital radius, altitude, and radius of planet. ORBITAL RADIUS = RADIUS OF PLANET + ALTITUDE So, when you get r in your Gravitational Strength equation (), you are actually getting the ORBITAL RADIUS, but if the object is on the surface of the planet Altitude = 0. A very good Universal Gravitational Problem/Solution (may/may not appear on the test or quiz)
Worksheet Solutions (CREDS TO ZACH KBAUM FOR #2 IN SET 2) NOTE FOR #1 IN SET 2 THE DIRECTION IS 22.5 DEGREES BECAUSE IF YOU LOOK AT MY VECTOR DIAGRAM(S) AND USE INVERSE TAN OF 3.54G/8.54G THE G S CANCEL OUT AND THE ANGLE IS 22.5 DEGREES. Set 1
Set 2 (#1-15 only)
Note: For problems 14 and 15, YOU CANNOT USE because it is NOT a circular orbit.
14. PE 0 + KE 0 = PE f + KE f ***NOTICE THAT THE MASS OF THE SATELLITE DOES NOT MATTER!*** Now, your initial radius is 10 7 meters, your initial speed is 800 m/s, and your final radius is 10 6 meters. So now all you need to do is substitute and get your final velocity (the one on the right side)! 15. a) PE 0 + KE 0 = PE f + KE f ***NOTICE THAT THE MASS OF THE SATELLITE DOES NOT MATTER!*** Now, your initial radius is 10 7 meters, your initial speed is 800 m/s, and your final radius is 10 6 + 5 x 10 5 meters because ORBITAL RADIUS = RADIUS OF PLANET + ALTITUDE (and when the satellite is on the planet s surface, altitude = 0. b) This problem is exactly the same as part a) except that REMEMBER AT MAXIMUM ALTITUDE VELOCITY = 0 SO YOUR EQUATION IS: PE 0 + KE 0 = PE f + KE f1 ***NOTICE THAT THE MASS OF THE SATELLITE DOES NOT MATTER!*** Now, when you substitute and find the final RADIUS, REMEMBER ORBITAL RADIUS = RADIUS OF PLANET + ALTITUDE.So you MUST subtract the RADIUS OF PLANET from your RADIUS to get the final answer.