Carry out the integration of eq. 14.7 in landau for u = -a/r. use the substitution u = 14.7 and show that u = (e/p) cos +(1/p) solves the integral. find p and e in terms of m, u, a and e. hint: multiply the numerator and denominator by r2 21. use p/r e cos 1 and your results from exercise 20 to show that e > 0 corresponds to a hyperbola e 0 corresponds to a parabola, and e < 0 corresponds to an ellipse. 22. there are plenty of asteroids flying around in the universe. for an asteroid coming from infinity with velocity v find the effective total cross-section for the asteroid to hit the earth (due to the gravita tional attraction between them). you can assume that the asteroid is much smaller than the earth what happens in the limit v = 0o? interpret the result hint: treat this as a scattering problem with the asteroids all moving in the same direction (as in a beam of particles), and compute the maximum impact factor for an asteroid to hit the earth, bmax the cross-section is then o = tb max