Circular/Orbital Motion Review

OPENING QUESTION: Working solo, see how far you can go in deriving Newton's form of Kepler's Law of Periods.

Make sure you update your CHROMIES!!! See slide #7

LEARNING OBJECTIVES: I will work with my team to review for tomorrows Unit Test

WORDS O' THE DAY:

  • Centripetal ("towards the center")
  • Centrifugal ("away from center")
  • Gravitational Constant: G = 6.674 × 10-11 Nm2/kg2
  • Period ("Time to complete one orbit")

FORMULAE OBJECTUS:

  • T2 ∝ A3: The square of the period (in years) of an object orbiting the sun is proportional to the cube of the average distance to the sun (in years). This is kind of archaic in that we rarely see the proportional symbol anymore.

  • T2 = a3: The square of the period (in years) of an object orbiting the sun is approximately equal to the cube of the average distance to the sun (in years). We MUST keep in mind this is an observational relationship. Although it gets us close (in most instances) it is not an exact value so the "=" sign isn't really appropriate although it is widely used.

  • MsT2 = a3: This version is still approximate but it allows us to substitute in the mass of *other* stars as long as we measure the mass of the other star in terms of the mass of the sun being 1.00

  • T2 = (4π2/GM)(a)3 = This version is much more accurate is often referred to as Newton's version of Kepler's Law. Notice ALL values must be in SIU

    • v2/r: centripetal acceleration
    • mv2/r: centripetal force
    • Fg = Gm1m2/r2: This is Newton's famous equation for gravitational attraction. The gravitational force between objects is found by multiplying the mass of each object by the "G" the gravitational constant divided by the square of the distance between those two masses in meters (square). Oddly enough, gravity is a very, very weak force. A simple bit of friction here on Earth causes objects to NOT be drawn together....we'll discuss at length

WORK O' THE DAY:

Let's work through the learning targets and make sure everything is comfy there.

After that we'll go through our 'usual' exercise of writing a series of easy and moderate problems based on those (Today's Opener is an example of a TOUGH problem)