November 2008 Sky from the Keeble Observatory
Some quick updates: The Hubble Space Telescope had a failure in the on-board
computer “Side A router” which communicates between the science instruments and
the telemetry, preventing the telescope from taking any data or relaying results
to the ground. All instruments have now been switched to “Side B” and the telescope
has resumed science activity. There was some trepidation about the switch-over,
since those backup circuits had not been tested since before its initial deployment
in April 1990. 18 years is a long time for electronics to sit unused! The next and
final servicing mission has been delayed from its initial October launch target,
likely until May to allow for the installation of a new router.
Mars Phoenix is running low on power as Martian northern winter drops overnight
temperatures into the -150 degree range. The probe has gone into “safe mode” because
of low power at least once, though it has recovered. The good news is that all the
major science tasks have been completed. Observing the onset of winter is “gravy”
to the mission team.
One could hope to apply the same idea of triangles to planets in the outer solar
system that we used for the inner solar system, but it doesn’t quite work. If we
observe a planet when it is 90 degrees away from the Sun in the sky, it is said
to be at quadrature. This duplicates the right triangle we drew last month
for the inner solar system, but … there are infinite possibilities for the distance
to an outer planet from this triangle, because we don’t know in what direction it
lies as seen from the Sun. So, instead of drawing triangles, we’ll measure these
distances with our clocks!
There are two relevant periods that we need to measure. One is the time it takes
for an outer planet to complete one orbit around the Sun. This is called its sidereal
period – sidereal means “relative to the stars,” so this is the period for
the planet to return to a given position relative to the background stars as seen
from the Sun. The other period is the time for the planet to return to the same
position relative to the Sun as seen from Earth. This is called its synodic
period. Let’s consider measuring from opposition to opposition (i.e. when the planet
is 180 degrees from the Sun in the sky and use this as our synodic period. It turns
out that there is a simple relationship between the synodic period and the sidereal
period. Let the synodic period be S, the sidereal period P, and let’s measure time
in years. (Earth’s sidereal period is defined as one year.) Then we have the following
relation: 1/S = 1 – 1/P. This gives us the sidereal period from observing the time
from opposition to opposition, i.e. the synodic period.
The next step is to look at the work of Kepler in the early 17th century.
He used observational data to determine that planetary orbits were not circles,
but ellipses. However, they’re close enough to circular for this discussion. Let
the radius of the orbit be A (technically we want the semi-major axis of
the ellipse). Kepler was able to show that there was a simple relationship between
A and the sidereal period, namely that the ratio between the square of the period
and the cube of the semimajor axis was the same for all the planets. We write this
as A3/P2 = constant. The easiest constant is to use the Earth-Sun
distance (1 astronomical unit, or 1 AU) and Earth’s sidereal period (1 year). Then
we can solve for the size of the external planet’s orbit, A, in multiples of the
distance from Earth to Sun. The last step is to adjust all these distances, which
are in AU in terms of more conventional units, like kilometers. We do this by bouncing
radar off those planets which reflect radar (Venus, Mercury, and Mars) and timing
the round trip for that signal. Knowing the speed of light, we now have the various
orbits calibrated into kilometers. So, how big is the solar system? We orbit an
average 150 million kilometers (93 million miles) from the Sun, taking one year
for a complete trip. Mercury lies only 58 million kilometers from the Sun, and orbits
in just 88 days. Jupiter, at 5.2 AU takes nearly 12 years for one orbit. Saturn
lies 9.6 AU from the Sun … a staggering 1.44 billion kilometers, or just under 900
million miles, and takes just under 29.5 years to go completely around. The most
distant “official” planet is Neptune, at 30 AU. We have identified a number of “dwarf”
planets, known also as plutoids, at larger distances. For example, Pluto
itself has an orbital period of 248 years, with a semi-major axis equal to 39.5
AU. Another is Eris’s 559 year orbit at nearly 68 AU (that’s 6.3 billion miles!).
Next month – on to the stars!
Lunar phases for November (all times are Eastern Standard): First Quarter
on the 5th, at 11:03 pm; Full Moon on the 13th, at 1:17 am;
Last Quarter on the 19th, at 4:31 pm; New Moon on the 27th,
at 11:55 am.
Pre-dawn planet watchers will have to settle for Saturn, high to the southeast,
about 47 degrees above the horizon at sunrise. It’s below Regulus in Leo. Mercury
rises about an hour before sunrise, but it will disappear into the Sun’s glare at
midmonth. By the end of the month, look for Saturn high to the south at sunrise.
At sunset, Jupiter and Venus are bright to the southwest. They’ll get closer together
as the month passes (see below). Mars is low on the west-southwest horizon at sunset,
but it’s unlikely you’ll pick it out of the horizon clutter and haze.
The almost full moon in the early morning hours on the 17th will make
the Leonid meteor shower a modest viewing experience, at best. Only the brightest
of these comet fragments will be bright enough to be visible. Nonetheless, if you’re
inclined to try, you’ll need to find a dark spot away from city lights. While the
“radiant” of this shower lies in the constellation Leo (which will be below the
Moon at 5 am on the 17th), you may be able to see some meteor activity
in any direction on the sky. The radiant is the direction from which the meteors
appear to originate.
Our overhead look at midmonth, about 2 hours after sunset, finds the Milky Way dividing
the sky roughly from northeast to southwest. The rather unimpressive constellation
Lacerta (the Lizard) is at zenith. Your eye is more likely to draw your attention
a bit to the west-northwest of zenith, where you’ll encounter Deneb, the brightest
star in Cygnus. About 45 degrees below zenith is Vega, which will be the brightest
star in this general direction, and likely among the first to emerge from twilight.
Below Vega, in a region of sky generally devoid of bright stars (you’re looking
out of the plane of the Galaxy), you’ll notice a modest diamond shape with four
stars marking the corners. This is Hercules. Binoculars pointed at the right-most
star will also pick out the globular cluster M13, just below and to the left.
To the northeast we find the familiar shape of Cassiopeia – here looking like a
back ward Greek sigma (S). Follow the lowest two stars up and to the right – on
a clear night you should see the faint patch marking the Andromeda Galaxy. It won’t
look as spectacular as the deep exposures printed in textbooks, but be reminded
that this is the most distant object you can see with your own eyes without a telescope.
It’s a system of several hundred billion stars, about 2 million light years distant.
To the southwest, those two brilliant “stars” are the planets Venus and Jupiter.
By month’s end, they’ll pass within about 3 degrees, with Venus the brighter of