CHAPTER 2
SOLAR SYSTEM, Part I
A. INTRODUCTION
In Chapter 1, we said the Sun and its satellites comprise a gravitationally
bound system called
the Solar System. The solar
system is gravitationally bound in the sense that the mutual gravitational
attractions between all
the objects in the system results in their moving in somewhat stable orbits
around a common barycenter.
That barycenter is located inside the Sun.
The radius of the Solar System may be defined as the distance
of the farthest object that is
orbiting the Sun.
This is a distance of about 100,000 AU. Hence, the radius of the solar
system is about 1.6 LY.
The most distant objects revolving around the Sun are comets.
B. LOCATING THE PLANETS IN THE SKY
For this material in detail, read the Introduction to Ex. 15.0 in the Course Manual.
B-1, Main Topics and Terms:
1. Ecliptic:The apparent path of the Sun around the celestial sphere relative to the fixed stars.
This apparent motion of the Sun along the ecliptic is a reflection of the
Earth's orbital motion around
the Sun. That is, because the Earth moves through an angle
of about one degree its orbit every day,
the Sun appears to move one degree eastward along the ecliptic relative
to the fixed stars.
Because
the Earth's axis of rotation is tilted by 23.5 degrees with respect to
the plane of its orbit
around the Sun, the ecliptic is inclined to the celestial equator by 23.5
degrees.
2. Elongation: The angular distance of an object eastward or westward from the Sun as measired along the ecliptic.
Study
the planar orbital diagrams on pages 113, and 117 in the Course Manual
intently and in detail.
Memorize the terminology shown in these planar diagrams of the orbits of
the planets. Also study the
chart on page 124 of the Course Manual. The latter shows how elongation
is measured along the ecliptic
on a rectangular star chart and is similar to the 2nd diagram below.
3. Zodiac: The band of 12 constellations girdling the celestial sphere and centered on the ecliptic.
4. Know definitions of Inferior and Superior Planets. See Ex. 15.0
5. Planetary
Configurations or Aspects: Conjunction, Quadrature, and Opposition
and associated
elongations. See Ex. 15.0.
The above diagram illustrates
how an observer measures elongation in the sky along the ecliptic
from the Sun. The
Sun does not have to be on the horizon.
B-2: Rules for measuring elongation
on a planar diagram of orbits:
1.
Draw a line from the Earth to the Sun and continue this line to the edge
of the chart.
Label this line 0o
2.
Draw a line from the Earth to the planet or the Moon.
3.
Draw an arcing angle between the above two lines with the arrow head at
the line drawn to the planet.
4. Set
the center of a protractor at the center of the Earth and align the zero-edge
along the line to the Sun.
5.
Read the elongation from the protractor where the line to the planet intersects
the
protractor scale.
6.
Determine whether the elongation is East or West.
Study the planar diagrams in Ex. 15.0 in the Course Manual.
B-3: Using a rectangular chart for measuring elongation:
The above diagram shows how elongation is measured along the ecliptic
on a rectangular chart of the
celestial sphere. The solid curve is the Moon's orbit.
The dotted curve with fiducial marks every ten
degrees is the ecliptic. Notice the Sun is always on the ecliptic.
The planet mercury (m) is depicted with
an elongation of about 12 degrees west of the Sun. Also see the
chart in Ex. 16.0, page 118.
B-4: Computing times of planetary events
There is a definite relationship between
a planet's elongation and what time it will rise, set,
or make upper transit (cross one's upper
local celestial meridian). For example, if a planet
has an elongation of 45o east,
it will rise, make upper transit, and set 3 hours after the
Sun rises, makes upper transit, or sets.
If the Moon has an elongation of 140 degrees West, what time will the Moon rise?
Step 1: Write down the correct equation:
Time of Moonrise = Time of Sunrise - TE
Step 2: Find the value of TE. To do this, divide the elongation by the rate of rotation of the
Step 5 (if necessary): Therefore, add 24 hours to this and we get 20:40.
So the most recent Moonrise was at 20:40 on the previous day.
In
the case where the elongation is East, a negative sign must be prefixed
to the value of TE when
substituting
this value in the above equation. In that case, minus a minus
elongation results in
adding
the elongation time to the time for the corresponding solar event.
Practice,
practice doing problems like the one above. Just change the elongation
and or
change
the event asked and follow the above procedure, step by step, to calculate
the answer.
Problems of this kind are done in Ex. 15.0
For example, do the following problems:
What
time does Jupiter set if it is at eastern quadrature?
What
time does the Moon rise if it has an elongatgion of 40o E?
If you have difficulties
doing these calculations, you should come to see me in my office for help.
1. One Star, the Sun. Everything else in the solar system is considered to be a satellite of the Sun.
2. Planetary Bodies
a. Major
Planets: There were 9, now there are 8 (Pluto demoted in 2006),
but we may continue to
call Pluto a planet. Can you name the major planets in order from the Sun?
The major planets move in nearly circular orbits, that is, in orbits that
are slightly elliptical.
This was discovered by J.ohannes Kepler in 1600.
b. Dwarf
Planets: A newly defined category as of Aug. 2006. There are
only 6 such bodies currently
listed in this category: Eris (formerly 2003 UB313 and originally
named Xena by
its discoverer, M. Brown at Cal. Tech.), Pluto, Ceres, Makemake,
and Haumae.
The above list shoul also include Makemake, and Haumae.
c. Minor
Planets (Asteroids): More than 390,000 have been discovered as of
2009 Most orbit the Sun between
Mars and Jupiter. The 4 largest are Ceres (now also a
dwarf planet), Juno, Pellas, and Vesta.
4. Comets number in
the billions; about 1000 have well defined orbits. Comets are
relatively small
bodies, both in size and mass, that are composed mostly of ice and dust
and move in very elliptical
orbits around the Sun. When a comet comes to within 5 AU
of the Sun, a tail develops.
5. Trans-Neptunian Objects
(TNOs). This is a new class of objects that have been discovered
since 1992.
They are small, solid bodies that move in nearly circular orbits
around the Sun beyond the orbit of Neptune.
TNOs
appear to possess a very thick upper layer of ice. More than 1000 such
bodies have been definitely
identified
but thousands may exist undiscovered.
TNOs
are also referred
to as Kuiper Belt Objects or KBOs if they are within 55 AU of the Sun.
This is because
in 1951, Gerard Kuiper postulated that there was a disk-shaped region of
comet nuclei that were orbiting the Sun
beyond the orbit of Pluto and extending to about 55 AU. So any objects
discovered to be in this region are
now also referred to as KBOs, even though they are not a comet.