Newton’s Laws

							   Astronomy                                                                                            Name:
   Graphing Newton’s Form of Kepler’s 3rd Law                                                           Period:

1. Suppose a new, super high-powered telescope is built and you have a chance to observe up close an extra-
   solar planet (a planet in another solar system) of unknown mass. You discover that this planet has a
   moon (which you name after your favorite high school astronomy teacher), and after many observations
   you plot the distance of this moon from the planet against time and come up with the graph below.


                                                       AOKeefius
                                                      ___________

                              4.0000
                              2.4E8

                              1.8E8
                              3.0000

                              1.2E8
                              2.0000
          Distance (meters)




                               6.0E7
                              1.0000                                                                        4 π2    a3
                                                                                                 P2 =
                                                                                                         G (m1+ m2)
                                  0
                              0.0000


                               –6.0E7
                              -1.0000

                              –1.2E8
                              -2.0000

                              –1.8E8
                              -3.0000

                              –2.4E8
                              -4.0000
                                         0.0
                                        0.0    0.25
                                               0.5     1.0
                                                       0.50      0.75
                                                                 1.5        1.00
                                                                            2.0    1.25
                                                                                    2.5   1.50
                                                                                           3.0
                                                              Time (days)




   a. What is the orbital period of this moon? _______________ days & _______________ seconds.



   b. What is the length of the semi-major axis of the moon’s orbit? _________________ meters



   c. What is the mass of the planet, assuming the mass of the moon is negligible? ______________kg




   d. How many times greater or less than Earth’s mass is this planet’s mass? ___________________
   Astronomy                                                                                  Name:
   Graphing Newton’s Form of Kepler’s 3rd Law                                                 Period:

2. Suppose a new, super high-powered telescope is built and you have a chance to observe up close an extra-
   solar planet (a planet in another solar system) of unknown mass. You discover that this planet has a
   moon (which you may name after yourself), and after many observations you plot the distance of this
   moon from the planet against time and come up with the graph below.



                                                _________________

                     2.0E9
                     16.0
                     1.5E9
                     12.0
                     1.0E9
                       8.0
      Distance (m)




                       .5E9
                        4.0                                                                                4 π2
                                                                                               P2 =                a3
                                                                                                        G (m1+ m2)
                         0
                       0.0
                     -.5E9
                      -4.0

                       -8.0
                     -1.0E9

                     -12.0
                     -1.5E9

                     -16.0
                     -2.0E9
                              0.0
                              0     2
                                    0.5   1.0
                                            4     1.5
                                                    6   2.0
                                                         8     2.5
                                                               10     3.0
                                                                      12    3.5
                                                                            14    4.0
                                                                                  16    4.5
                                                                                        18
                                                        Time (days)


   a. What is the orbital period of this moon? ___________________ seconds


   b. What is the length of the semi-major axis of the moon’s orbit? _________________ meters


   c. What is the mass of the planet, assuming the mass of the moon is negligible? __________________kg




   d. How many times greater or less than Earth’s mass is this planet’s mass? ________________________