# Relativity, Gravitation and Cosmology

Solutions

2005 solutions: When I already had solutions from the 2004 class I just indicated the correspondence. The 2004 solutions are included below. "tba" means solution is to be added.

hw1
2-7, 5-1, 5-3, 5-13, 5-14 in hw1-2004
1-S (relativistic beaming)

hw2
6-14, 7-11, 7-12, 2S-3 in hw2-2004.
2S-1,2 tba

hw3
1, 2 tba
3 in hw3-2004

hw4
9-10 and 12-6 in hw4-2004
9-18 and 4S-1 tba

hw5
2-10, 12-11, 15-6  tba
15-10, 15-18 in hw5-2004 (first and last problems).

hw6
13-7 tba
15-16 in hw6-2004
6S-1 is hw7-2004, Problem 5.
6S2,3,4 tba

hw7

16-7, 16-13, and 6-14 in hw8-2004.
7S-1 asked to derive (16.8) using the Lagrangian method. The argument is this: The Lagrangian is -tdot^2 + (1+f)xdot^2 + (1-f)ydot)^2 + zdot^2, where f=f(t-z). The Euler-Lagrange eqn for x says (1+f)xdot is constant, so if xdot=0 initially, it remains zero.

7S-2 in hw7-2004, Problem 1 (that does not include this year's part (b), the charge dipole).

hw8
See hw8-2004. hw8 this year corresponds to problems 4,5,6,7. The original solution of 18-3 missed a required division by dt/d\tau, which is corrected in the "18-3 corrected" link here.

hw9
See hw9-2004 (Includes also 18-28 which was not assigned this year, and therefore problems 8 and 9 correspond to this years 7 and 8.)

hw10 19-6 and 19-7 are in hw10-2004; 10S-1 and 10S-2  are here and called 1 and 2 (from hw11-2004).

hw11  Problems 3-6  (Numbered differently from this year; 1 & 2 are omitted. let me know if you want solutions.)

hw12
PDF file  (In correct order, but numbered differently from this year.)

hw13

2004 solutions:

hw1
hw2
hw3 , hw3errors
hw4
hw5
hw6 , P1 alternate
hw7
hw8 , problem 18-3 corrected
hw9: page 1, page 2, page 3, page 4
hw10
hw11

hw12
hw13