2. Show that the total gravity experienced by the test particle is F= (G*M*m)/ (p*(p^2+L^2)^1/2).

a). Show detailed steps on how the integral is constructed from Newton's Law of Gravity.

3. Find the Taylor series expansion of F near L/p=0 ( i.e. a power series of L/p.) You must display the first three non-zero terms. Then, use this Taylor series to show that

F= (G*M*m)/p^2 [ Linear Approximation]

when L p ( L/p0 ).

4. Error Estimate. How good is the approximation in question 3) if L=300 km and p =5,000km ? Estimate an upper bound of the relative (percentage) error.