December 2010 Sky from the Keeble Observatory
We’ve spent several columns on using the Doppler effect to measure radial velocities,
and then infer the masses of stars and planets. With thousands of stars to study,
we learn that all of them have virtually the same chemical composition – essentially
90% hydrogen, 9% helium, and 1% “metals,” i.e. everything else on the periodic table.
These values are counting atoms. If we go by mass, the numbers are more like 70%
hydrogen, 28 % helium. We also learn that main sequence stars of the same mass have
the same surface temperature and luminosity, which means they are the same size.
Effectively, knowing the mass tells us everything!
We can apply basic understandings from physics to write down a set of stellar structure
equations, use them to model the characteristics of a star with given mass
and composition, and determine that our models for that mass have the properties
we actually observe. Understanding the nuclear processes which release energy at
the stellar core also allows us to make a time series of models as the core consumes
its hydrogen fuel, and from that to determine how the star will change over its
lifetime. (We refer to these changes as stellar evolution. The term may be
unfortunate, since it calls to mind the process of biological evolution, which deals
with changes in species over time. Stellar evolution deals with changes in individual
Let’s follow the evolution of our own Sun (and other stars of the same mass!). We
start with one solar mass of hydrogen, helium, and metals with solar abundances
throughout. (We use surface abundances. Since only the core (inner 10%) participates
in nuclear fusion, the surface composition is essentially unchanged. This so called
Zero Age Main Sequence model tells us that the Sun was initially a bit smaller
in radius (~ 87%), with smaller luminosity (~ 70%), and a surface temperature a
few hundred degrees cooler than its present 5800 K. As core hydrogen is consumed
the star slowly increases in size, temperature, and luminosity, reaching current
values in about 5 billion years. The core today is more helium than hydrogen, with
64% of the mass in helium and only 34% hydrogen. Obviously this trend cannot continue
Once the core helium is exhausted, the nuclear “fires” will cease. This will take
place in about 5 billion years from the present. Denied an energy source to maintain
pressure, the core will begin to shrink. This shrinking comes at the expense of
gravitational potential energy, so the core actually gets hotter. Enough so that
the region just outside the core continues to fuse hydrogen in a “shell source.”
This shell is hotter than the original fusion core, and the reaction proceeds at
a higher rate. The star reacts to this increase in luminosity by expanding its envelope
which, ironically, cools the surface. We have here a red giant – a one solar
mass star with a cool photosphere and radius approximately the size of the orbit
of Mars. This state will last about a billion years. Next month, we’ll follow the
evolutionary track to its ultimate end.
Lunar phases for December: New Moon on the 5th, at 12:36 pm; First
Quarter on the 13th, at 8:59 am; Full Moon on the 21st at
3:13 am; Last Quarter on the 27th, at 11:18 pm. All times are Eastern
The Full Moon will be accompanied by a total lunar eclipse. The Moon will enter
the umbra (darkest part of Earth’s shadow) at 1:32 am – this event is called
“first contact.” Totality begins at 2:40 (“second contact”), but the Moon will still
be visible because of sunlight refracted through Earth’s atmosphere. It will appear
reddish – think of a million sunsets and sunrises. Totality will last until 3:51
as the Moon begins to emerge from the umbra (“third contact”), and the umbral eclipse
will end at 4:59.
The 21st is also the Winter Solstice, when the Sun is at its most southern
position in the sky, directly over the Tropic of Capricorn at 6:38 pm EST.
Predawn planet watchers will have no difficulty seeing Venus and Saturn to the southeast.
Venus will be at its brightest on the 4th, but it will still outshine
everything else in the sky. Venus rises about 4 am, and will be about 23 degrees
above the horizon early in the month, with Saturn above and slightly to the south
at 37 degrees. By the end of the month they will both be higher, but still separated
by about 13 degrees. Mercury returns to the early morning skies by the end of December,
rising about an hour before sunrise.
Jupiter emerges from evening twilight to the south, beginning the month about 40
degrees above the horizon and climbing closer to 50 degrees by the end. Uranus is
less than a degree above Jupiter, about 1½ times the width of the Moon. You may
be able to see it in a small telescope, but it will not be nearly as bright as Jupiter
(nor as interesting to look at!). Mars is too close to the Sun’s glare to be seen
About 2 hours after sunset at mid-month we find the constellation Andromeda at zenith.
About 5 degrees north of zenith you may be able to see the Andromeda Galaxy. Even
with a small telescope it won’t impress like the photographs you may have seen,
but it remains the most distant object visible to the naked eye. Doppler measurements
tell us that it is one of the few galaxies moving toward the Milky Way (recall that
most are receding, caught up in the universal expansion). Its line of sight velocity
is 300 kilometers per second, which will bring it into the vicinity of our home
Galaxy in about 5 billion years. We don’t know its tangential velocity, so there
may not be a direct hit this time, but eventually the two galaxies should merge
and form a giant elliptical galaxy.
Cygnus is to the west-northwest, standing normal to the horizon at the “northern
cross.” Deneb is the bright star at the top, about 42 degrees above the horizon.
Albireo marks the foot of the cross at 20 degrees. Below and to the right you’ll
see the bright blue star Vega. Cassiopeia is due north, above Polaris. Its familiar
shape now looks like a crooked M. Orion is rising to the east, below Taurus and