1:  Considering the Archimedean Spiral pattern of the interplanetary magnetic field (IMF),

                  r - r_o = -v/w (q -q_o),

(a) What is the rotation rate of the Sun (w) in radians/s, if it rotates once every 27.5 days?
(b) Which longitude at the Sun would be "best connected" to the Earth at 1 AU for a typical solar wind speed of 400 km/s?  For a slow wind speed of 300 km/s?  For a fast wind speed of 600 km/s?  Is this longitude east or west of the solar central meridian?

2: According to the information by Ian Axford and Steve Suess, the "ram pressure" of the solar wind can be approximated by

P = nmv²/R²,

where n is the ion number density at 1 AU (about 8 x 10⁶ m^-3), m is the average ion mass (use the proton mass, 1.67 x 10^-27 kg), v is the speed of the solar wind (about 400 km/s), and R is the distance in AU. Thus, the ram pressure falls off with distance from the Sun, resulting in a termination shock with the ram pressure equals the pressure of the interstellar medium. The properties of the interstellar medium have not been measured, but earlier estimates suggested B = 0.6 nT, T = 7000 K, and particle number density n = 10⁵ m^-3. (a) Use the interstellar medium estimates to calculate the gas pressure of the interstellar medium, P_g = nkT. (b) Also calculate the magnetic pressure of the interstellar medium, P_mag = B²/2m₀. Which is the dominant type of pressure? (c) Combine the two to get the total pressure, P = P_g + P_mag, and use it in the above expression to solve for the distance to the termination shock, in AU. (d) The Voyager measurements show that the termination shock is actually about 90 AU. What value for the interstellar magnetic field strength would you infer from this?