(a) If the radius of the planned orbit is **R**, use Newton's laws to show each of the following.

(c) Suppose that the injection of the satellite into orbit is less than perfect. For an injection velocity that differs from the desired value in each of the following ways, sketch the resulting orbit on the figure. (**J** is the center of Jupiter, the dashed circle is the desired orbit, and **P** is the injection point.) Also, describe the resulting orbit qualitatively but specifically.