Stellar Masses and Distances Worksheet
Name Leah Walker
Please answer in complete sentences and show all calculations in detail.
Part 1:
For stars on the main sequence, luminosity (expressed in units of the Sun’s luminosity, L
⊙
) varies as the fourth
power of the mass (in units of the Sun’s mass, M
⊙
)
L
M
4
If a main sequence star has a mass of 3 M
⊙
, how much more luminous will it be compared to the Sun?
L = (3
M
⊙
)^4 = 52
If two main sequence stars differ in mass by a factor of 2, by how much would they differ in luminosity?
L2/L1 = (M2/M1)^4
L2/L1 = (2)^4 = 16
In a binary star system, each star orbits the common center of mass (barycenter). Newton’s reformulation of
Kepler’s third law can be used to determine the combined mass of the stars if we know the semi-major axis of
the orbit and the orbital period. For the mutually orbiting stars, the orbital period (P) is the period with which
they go around each other and the semi-major axis happens to be the separation distance between the stars,
which we can call (d), so that the equation can be written as,
d
3
= (M
1
+M
2
)P
2
where
d
is in astronomical units (AU),
P
is in years (yr) and the mass is in solar mass units (M
⊙
).
A distant star and its companion are separated by about 11 AU and have an orbital period of about 27 years.
Calculate the combined mass of the system.
d
3
= (M
1
+M
2
)P
2
11
3
= (M
1
+M
2
)27
2
