The distance to the star in parsecs is given as 20 pc.
Using the absolute magnitude (M) and apparent magnitude (m) relation, we can find the star's apparent magnitude:
m - M = -5 + 5 log(d)
where d is the distance to the star in parsecs.
Plugging in the values we have, we get:
m - (-0.66) = -5 + 5 log(20)
m = 3.34
Therefore, this star's apparent magnitude is 3.34.
The star's luminosity is 160 times that of the Sun.
Using the Stefan-Boltzmann law, we can find the star's radius:
L = 4πR²σT⁴
where L is the luminosity, R is the radius, σ is the Stefan-Boltzmann constant, and T is the surface temperature.
We can write the ratio of the star's luminosity to that of the Sun as:
L/Lsun = (R/Rsun)²(T/Tsun)⁴
Plugging in the values we have, we get:
160 = (R/Rsun)²(4000/5800)⁴
Solving for R, we get:
R = 10.7 R⊙
Therefore, this star's radius is 10.7 times that of the Sun.
Using Wien's law, we can find the wavelength at which the star radiates the most energy:
λmax = 2.898 × 10⁶ / T
Plugging in the values we have, we get:
λmax = 724.5 nm
Therefore, this star radiates most of its energy at a wavelength of 724.5 nm.
The star's surface temperature is 4000 K.
Using the Harvard spectral classification system, we can find the star's spectral class based on its surface temperature:
O B A F G K M
50,000 10,000 7500 6000 5200 3700 2400
The star's surface temperature falls in the range of a K-type star.
Therefore, this star's spectral class is K.
Finally, we can use the definition of parallax to find the star's parallax:
p = 1/d
where p is the parallax in arcseconds and d is the distance to the star in parsecs
