The Chronos-II space observatory uses stellar parallax with a precision of 1.6×10−41.6 \times 10^{-4}1.6×10−4 arcseconds to measure the distance to nearby stars.
One of the target stars in its initial survey is the massive hot star Xylar-9. Data gathered for Xylar-9 is compiled in the table below:
| Parameter | Value |
|---|---|
| Parallax angle | 6.4×10−46.4 \times 10^{-4}6.4×10−4 arcseconds |
| Radius of star | 2.2×1010 m2.2 \times 10^{10}\text{ m}2.2×1010 m |
| Mass of star | 6.4×1031 kg6.4 \times 10^{31}\text{ kg}6.4×1031 kg |
| Surface temperature | 12500 K12500\text{ K}12500 K |
| Temperature of the stellar atmosphere (corona) | 4.8×106 K4.8 \times 10^6\text{ K}4.8×106 K |
Estimate the maximum stellar distance in parsecs (pc) that can be measured using the Chronos-II observatory.
Calculate the percentage uncertainty in the calculated distance of Xylar-9.
A stellar wind consisting of high-energy charged particles flows continuously from the star's corona into interstellar space. These particles include protons of mass 1.67×10−27 kg1.67 \times 10^{-27}\text{ kg}1.67×10−27 kg. Assume the stellar atmosphere behaves as an ideal gas.
Show that the typical kinetic energy of a proton in the atmosphere of Xylar-9 is approximately 1.0×10−16 J1.0 \times 10^{-16}\text{ J}1.0×10−16 J.
The gravitational potential energy of a proton at the base of the star's atmosphere is −3.2×10−16 J-3.2 \times 10^{-16}\text{ J}−3.2×10−16 J. Calculate the gravitational potential energy UUU at the maximum radial distance from the star that a proton with this average kinetic energy could reach.
Calculate the distance from the centre of the star reached by this proton.
Explain why the star has a stellar wind that reaches much greater distances from the star than the distance calculated in (b)(iii).
