# Solutions

1. The photo below shows the constellation Orion. Bellatrix is the star on Orion's left shoulder.

The following data is copied from wikipedia

Distance from Earth = 77Pc

Radius = 6R_{sun}

Luminosity = 6,400 L_{sun}

Temperature = 22,000K

Apparent magnitude = 1.64

a. Show that the absolute magnitude of Bellatrix is -2.73

b. Use Stefan Boltzmann Law and the radius to calculate the Luminosity. Compare this with the data.

c. Given that a star with apparent magnitude 0 has brightness 2.32 x 10^{-8} Wm^{-2} find the brightness of Bellatrix and hence its Luminosity. Compare this with the data.

The values do not seem to agree. Why might this be?

Solution

2. The star in the photo below is Beta Pictoris.

a. If the angular displacement of a telescope when pointing at the Beta Pictoris on either side of the Earths orbit around the Sun is 51.44 milliarcseconds show that its distance from the Earth is about 60 light years.

b. The peak in the spectrum of Beta Pictoris is at 360nm. Show that its temperature is 8000K.

c. The apparent magnitude of Beta Pictoris is 3.861, given that the brightness of a magnitude 0 star is 2.32 x 10^{-8} Wm^{-2} and the luminosity of the Sun is 3.8x10^{26 }W show that the Luminosity of Beta Pictoris is about 8 L_{sun}

d. Give that the radius of the sun is 7 x 10^{8} m, use your answers to the previous questions to show that the radius of Beta Pictoris is about 1.5 r_{sun}

Solutions