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					                                                         Overview
 Gravity and Kepler’s
                                             In this section:
         Laws                                  What is gravity and how does it work?
                                               How do objects move in the solar system?

               PSC 203                       Pre-
                                             Pre-lecture questions …




                                                 Theory of Gravity
                                             Gravity is the force of attraction
         Gravity                             between any two masses

                                             Sir Isaac Newton
                                             Albert Einstein




      Law of Gravity                          Qualitative relationships
Force is:                                    Mass
directly proportional to product of masses     More mass, more force
inversely proportional to distance squared     Less mass, less force
                                             Distance
                                               Large distance, less force
                                               Small distance, more force




                                                                                          1
                           G                                Qualitative Example
Universal Gravitational Constant                                 G mA m2               G 2m A m 2
found by experiment                                        FA=          2
                                                                                 FB=             2
                                                                    r                        r
assumed constant throughout universe


                                                                    F B= 2F A
Don’t need to memorize this number




               Example 2                                    Qualitative relationships

        G m1m2                           G m 1m 2          Need to look at full equation
FA=                              FB=               2
                                                           You need to make sure that your units are
             r2                               3r           the standard mks (meters, kilograms, and
                                                           seconds)
                                                           Then it is just plugging into the calculator
                             1
               FB=             F
                             9 A                           For astronomy, masses and distances are
                                                           often found in the tables in the book




Example: Earth and Moon

                      Nm 2                                           Surface Gravity
       (6.7 x10 −11        )(6 x10 24 kg )(7 x10 22 kg )
                      kg 2
FG =
                         (4 x108 m) 2


         FG = 1.75x1020 N




                                                                                                          2
           Surface Gravity                Qualitative relationships
Measures the affect                      Mass
of gravity at the                          More mass, more gravity
surface of an object
                           GM              Less mass, less gravity

Depends on mass and
radius of planet
                         g= 2            Radius
                                           Large radius, less gravity
                           R               Small radius, more gravity




            Give and take                         Example questions

The jovian planets have more mass than   From concept tests…
terrestrials
But they also have a larger radius…

So what is the result?
  Table from other textbook




                                                        Kepler
    Kepler's 1                1st                        (1571-
                                         Johannes Kepler (1571-1630)
                                         was trying to understand how planets
       Law                               moved
                                         used very precise data from Tycho Brahe




                                                                                   3
      1st observation                              Kepler's 1st Law
 converted observations of positions of
 planets against background stars to
                                              “Each planet moves in an
 positions relative to sun                    elliptical orbit with the sun
 didn't fall on perfect circles as had been   at one focus of the ellipse.”
 assumed




                 Ellipse                               Eccentricity
oval shape                                    eccentricity - a measure of the flattening
                                              of an ellipse
2 focus points
                                              e = 0 is circle
mathematical
equation                                      e > 0 means flattened
                                              higher e means more flattened




Eccentricity of objects
 most planets have low eccentricity (e <
 0.1)
                                                Kepler's 2nd
 comets have high eccentricity
 applet
                                                   Law



                                                                                           4
     2nd observation                           Kepler's 2nd Law
Planets didn't move at a constant speed    “The line from the sun to any planet
                                           sweeps out equal areas in equal time
moved faster when closer to sun
                                           intervals.”
moved slower when further from sun




          Animation
Links to animation applets are on course
website
                                              Kepler's 3rd
applet
                                                 Law




     3rd observation                           Kepler's 3rd Law
planets did not orbit around sun at same    “The squares of the periods of
speed
                                            the planets are proportional to
closest to sun orbited faster                  the cubes of the average
further out from sun orbited slower            distances from the sun.”
                                                         P2 ~ a3




                                                                                  5
      Animations                              Using the equation
Links to animation applets are on course   Most often use the ratio form of the equation
website
applet                                                   2           3
                                                     P   1
                                                             =   a1
                                                         2        3
                                                     P   2       a   2




Example: Planets around Sun                Example: Planets around Sun

For Earth:                                 For an object at, a = 2AU
  P2 = 1 year
  a2 = 1 AU                                 a 3 = ( 2) 3 = 2 ∗ 2 ∗ 2 = 8
For any other object:


             P= (a∗a∗a)                        P = 8 = 2.83
P in years, a in AU




         Example question

From concept tests….




                                                                                           6

				
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