(3 points] [Russel], P5?) The location of the heliospheric boundary, where the pressure of the solar wind and the interstellar plasma are in balance, depends on both the solar wind properties and the external [local interstellar medium [LISMD properties. (a) Assume a setting where the LISM (mainly hydrogen) gas density is nag\": = 1 ram3 and that it is 1% ionized, has a plasma temperature of To = 100 K, a magnetic eld strength of 3;; = 0.01 nT. Calculate the total pressure [thermal Pm" plus magnetic Pm]. Is this LlSM a high or low beta medium? Now assume the interstellar medium ows at v0 = 10 km! 3 parallel to the magnetic eld. What is its dynamic pressure? Which of the three pressures is dominant? (b) Assume a star with a cold, weakly magnetized hydrogen plasma wind and a proton density of n,- = 10 CHI3 at lAU owing radially outward at v,- = 200 km! s is within this LISM. Where (in AU] is the as- tropause (where the internal, dynamic pressure-dominated, and external pressures balance as a func- tion of the angle away from the interstellar ow direction? Describe the general shape of the resulting astrosphen? [approximate astrocentric radius, R, in the ow direction, ank, and wake directions) based on these ideas of internal! external pressure balance. How is this changed if the stellar wind speed is increased to 600 km! sec and its density at 1 AU is reduced to 0.01 cm'3