Download 2.64 3.26156 8.61 pc ly × =

Astr 2020 Problems in Stellar Astronomy
Homework Set 5 Solutions
Chapter 13 # 45, 48, 49 & 50
13.45. Sirius, the brightest star in the sky, has a parallax of 0.379 arcseconds. What is
the distance in parsecs? In lightyears?
d (parsec) 
1
 (arcsec)

1
 2.64 pc
0.379arcsec
2.64 pc  3.26156 ly pc  8.61ly
13.48. Sirius is 22 times more luminous than the Sun, and Polaris (the “North Pole
Star”) is 2350 times more luminous than the Sun. Sirius appears 23 times brighter than
Polaris. How much farther away from us is Polaris than Sirius? What is the distance of
Polaris in lightyears?
Set the problem up as a ratio of brightness’s:
LS
BS
BS LS rP2
4 rS2



BP LP
BP LP rS2
4 rP2
22 LSun rP2
rP
23
2350  23



rS
1 2350 LSun rS2
22 1
rP
 49.6
rS
Thus Polaris is about 49.6 times farther from us than Sirius. From Appendix 5 of
the textbook, Sirius is 8.58 ly from Earth so Polaris is 8.58 ly X 49.6 = 425 ly
away.
13.49. Proxima Centauri, the star nearest the Earth other than the Sun, has a parallax
of 0.772 arcseconds. How long does it take light to reach us from Proxima Centauri?
d (parsec) 
1
 (arcsec)

1
 1.295 pc
0.772arcsec
1.295 pc  3.26156 ly pc  4.225ly
Since it is 4.225 lightyears away from us it will take light 4.23 years to reach us.
13.50. Betelgeuse (in Orion) has a parallax of 0.00763 ± 0.00164arcsec, as measured
by the Hipparcos satellite. What is the distance to Betelgeuse, and the uncertainty in
that measurement?
d (parsec) 
1
 (arcsec)

1
 131 pc
0.00763arcsec
Find the uncertainty as a fraction of the parallax angle and then multiply the
calculated distance by that fraction to get the uncertainty in pc.
0.00164arcsec
 0.215
0.00763arcsec
0.215 131 pc  28.2 pc
so
Distance to Betelgeuse = 131  28.2pc