Question

The Gaia satellite will measure parallaxes with an accuracy of 2 × 10⁻⁵ arcsec for stars with V < 15.

(a) What is the distance d of an M5 I supergiant with log(L/L_ʘ) = 5.50 and BC = −3.70 that has V = 12, if the effect of interstellar extinction is ignored?

(b) What is the relative distance accuracy σ(d)/d of such a star?

(c) Assuming that T_eff is known, what is the relative accuracy in radius σ(R)/R?

Answer 1

Given that

BC=-3.70

v=12

log(L/Lo)=5.50

ANSWER Given that O = 9x10 arcsec a) BC = -3.70 8=12 we know BC = mbol-v mol = TBC -12-3.70 mbok = 8.3 - (mg-mi)/5 ALSO FL= 100 m2 F2 -1 (на L2 HTME = 100 (m2-mills → x des = toome - mi)/5 d2=1 AU me=-26.74 Let q fot sun. 2 (-26.74-31 X (IAU) ? TE = 1004-26.74-8.35

To como 100(–35.0u) 5 to a Camuge 104-7.08) Apply log on both sides logo (to) + 195, (194) 3 1050(106-7608) 5.50 +2 109,0 ( = 2467.008) 2 10910(au) = -14.016-5.50 ? 109,0 (IAU) = -19.516 10510 ( 1 ) = -1 ISO : 200 = 10(-19-51612) JAU = 106-19-51612) de d, - TAU (-19-516/2).

d=5.72 x 10" AU -5.72 x 10 pc 206265 E12A768.9 84 7284 Loh pe = 9.7731 x 109 x 105 pc d = 2.8x104 PC b) old) - 5 = 5x104 PC i old)/d = 5x 2.SXICWS 1.78 PC c) L= 4TR Tent o(R) R LE(L) For more in the last ofan)"

L), L+ d² - Tdt = (d)) ? - L+ (1) e-d12 ) ( 2) It ) arte = 1- (+1.49) 지