Keeble Observatory
July 2010 Sky from the Keeble Observatory
Last month we described measuring distances to stars. We applied a method known
as geometric parallax, which is a fancy way of saying that we draw triangles. Knowing
the size of Earth’s orbit and measuring the slight shift in direction to a star
over a 6 month period, we can calculate its distance in parsecs. We can use this
for stars out to about 300 light years. Now that we know the distance, what else
can be learned? It turns out that we can learn a lot.
The 19th century saw the development of spectroscopy. Passing light through
a prism dispersed it according to wavelength, i.e. color. (Today, we’re more likely
to use a “grating” to accomplish this … notice the multicolored reflections from
a CD or DVD.) We can measure the intensity as a function of wavelength to characterize
the spectrum, a technique which dates to the mid-1800s. It turns out that all objects
with temperatures above absolute zero emit continuous radiation across all wavelengths,
with the actual distribution of energy determined by the temperature of the surface.
Overall brightness is governed by Stefan’s Law, which tells us that the intensity
per unit area is proportional to the fourth power of absolute temperature. This
is why sunspots appear dark, even though the gas in that part of the solar surface
is still over 4000 K, because the rest of the solar surface is at nearly 6000 K,
making it about five times brighter. The peak intensity in the spectrum is governed
by a relation known as Wien’s Law, which says that the product of the temperature
and the wavelength at peak intensity is a constant. Thus, hotter objects emit a
greater fraction of their energy at shorter wavelengths. From a practical standpoint,
this means that if we determine the peak wavelength we know the temperature. Thus,
from the spectrum we determine a star’s temperature.
But, we can know even more. Combining our knowledge of distance and temperature,
we can also determine the size of the star. Stefan’s Law tells us the overall brightness
at the star’s surface, and the total luminosity depends as well on its surface area.
We measure its apparent brightness at our telescope, which depends on both the luminosity
of the star and the inverse square of the distance. So now we know distance, temperature,
and radius. In addition to the continuous part of the spectrum, we also know that
each chemical element has a characteristic discrete spectrum – i.e. only certain
wavelengths are present. If we look at a hot surface through a hot gas, what we
see is the continuous spectrum of the surface, minus the discrete spectrum that
would be emitted by the gas alone, which also depends on temperature. This means
that the absorption spectrum can be used to measure the temperature and composition
of a star’s atmosphere. This evidence tells us that all stars are mostly hydrogen
and helium, with the rest of the chemical elements a mere trace. If we’re counting
atoms or their nuclei, 90% of everything is hydrogen, and about 9% is helium.
So, now we know a star’s distance, size, and what they’re made of. Not bad for capturing
a little light and asking it lots of questions. Next month we’ll discuss determining
stellar masses.
Lunar phases for July: Last Quarter on the 4th, at 10:35 am; New
Moon on the 11th, at 3:40 pm; First Quarter on the 18th, at
6:11 am; Full Moon on the 25th at 9:37 pm. The New Moon is accompanied
by a total solar eclipse, but you’ll have to be on a boat in the South Pacific to
see it!
Predawn planet watchers will find Jupiter the only bright target this month. Look
for it high to the south-southeast early in July. With good binoculars or a modest
telescope you may be able to find Uranus about 2 degrees to the right. Jupiter will
move progressively to the west relative to the horizon, finishing the month at morning
twilight about 45 degrees off the south-southwest horizon. Evenings are better for
planets this month. Early in July, evening twilight finds Saturn, Mars, and Venus
arrayed in a line. Saturn is at 45 degrees to the southwest, Mars south-southwest
at 40 degrees, and Venus is brilliant 30 degrees above the western horizon. Mercury
is west-northwest, but too low to see. Venus, Mars, and Saturn move closer on the
sky, finishing the month with Mars and Saturn about a degree apart, emerging from
evening twilight about 30 degrees above the south southwest horizon. Venus is 6
degrees to the right and a little below, but it will be so bright it won’t be hard
to notice. Mercury will climb to about 15 degrees above the western horizon at sunset
by month’s end.
Our overhead view at mid-month finds the constellation Hercules at zenith about
two hours after sunset. Binoculars will allow you to pick out M13, a globular cluster
orbiting our Galaxy, almost directly overhead. Sweeping our attention toward the
east, we encounter Vega, the brightest star in the constellation Lyra, about 20
degrees from zenith. Binoculars or a small telescope directed to this constellation
will also pick out the faint smoky Ring Nebula, the remnant of a star once much
like the Sun. Below Lyra we find the familiar constellation Cygnus, about 50 degrees
above the horizon. In this orientation it’s not difficult to imagine this as a stick
figure of a flying swan. Deneb, to our left, marks the swan’s tail, while the colorful
binary Albireo marks the swan’s head toward the right.
To the south lies bright red Antares (Mars’ rival). Its color and brightness are
similar to Mars, but remember that Mars is now toward the west. To the northwest
we see the familiar asterism known as the Big Dipper, which is actually part of
Ursa Major. The “bowl” of the dipper is low, and the “handle” arches back toward
Arcturus, a50 degrees above the west-southwest horizon. (I use this description
as a mnemonic to help me remember how to identify Arcturus!). Harder to pick out
is Ursa Minor, the Little Dipper, since none of this constellation’s stars are particularly
bright. Try to see this dipper standing on its handle, with Polaris at the end and
the smallish bowl directly above.
Copyright 2010
George Spagna