Name:____________________________  Lab Section: Online  Date: _____________

Questions

1.                  Verify Kepler's first law by choosing two positions on the orbit. The geometrical definition of the ellipse is that the total distance from one focus to a point on the ellipse (L1) and back to the other focus (L2) must be the same for any point on the ellipse. An example of L1 and L2 is in Figure 1.  Show your work on the orbit plot (p. 3) and explain the results below. Calculate the eccentricity of the orbit.

Point 1           L1 =                       L2 =                       L1 + L2 =                             

Point 2           L1 =                       L2 =                       L1 + L2 =                             

                        e =                                          

2.                  Verify Kepler's 2nd law by the method of equal areas. Show your work on the Orbit plot (p. 27) and explain the results below.

Area 1      Base =                        Height =                        Area =                       

Area 2      Base =                        Height =                        Area =                       

3.                  At what point in its orbit is Explorer 35 moving with the greatest speed? (periluna or apoluna)

4.                  Using Kepler's 3rd Law () calculate the orbital period of Explorer 35. Complete the following steps (use scientific notation where appropriate):

a. ______________ cm      Measure the Moon's diameter from the orbit (p.27).

b. __3,476,000_____ m      Diameter of the moon in meters (textbook).

c. ______________ cm/m  Determine the scale factor

            (Divide the result in 4a by the result in 4b.)

d. ______________ cm      Measure the semi-major axis from the orbit (p. 1).

e. ______________ m        Determine the semi-major axis in meters.

            (Divide the result in 4d by the result in 4c.)

f. ______________ m3        a3 - Semi-major axis cubed

            (Multiply the result in 4e by itself three times)

g. ______________ sec2    Multiply k times a3.

            (8.02 X10-12 sec2/m3) X the result in 4f.

h. ______________ sec     Determine the orbital period in seconds.

            (Take the square root of the result in 4g.)

i. ______________ hours  Determine the orbital period in hours.

            (Divide the result in 4h by 3,600 sec/hr.)

5.                  Find the mass of the moon (in kilograms) using the Newtonian form of Kepler's third law. The third law is given by

,

            where                              

For (m+M) we can safely ignore the mass of the satellite (m) compared to the mass of the Moon (M), so the equation now looks like

Rearrange the equation to solve for M, insert the values of P2 (part 4g) and a3 (part 4f), and solve.  Show your work.