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.
 

Example of Computing Time of a planetary event, using the relation:
                                            Tp = TS - TE
(The symbols in the above equation are defined in Ex. 15.0 in the Course Manual.)

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

Earth, viz., 15 deg/hr.   We get: +140/15 = +9 and 5/15 hours. A fifteenth of an hour is 4
minutes (60/15).  Therefore, the elongation of the Moon in time units, or TE, is 9h20m W.

Step 3:  We assume the Sun always rises at 6:00 and sets at 18:00 for simplicity. So in this
problem, the corresponding solar event to Moonrise is Sunrise or 6:00.

Step 4:  Insert the numerical values into the equation and do the calculation.  Then we get:
 
  Moonrise = 6:00 - (+9:20) = -3:20.

Now there can not be such a thing as a negative time. The negative sign means we went back past
midnight into the previous day.

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?

What time does Saturn rise if it has an elongation of 150o W?

If you have difficulties doing these calculations, you should come to see me in my office for help.
 

C.  INVENTORY

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.
 

3. Planetary-like Bodies
   a. Moons: satellites of planets. There are >300 moons of the major planets; some of these are
       larger than some of the major planets. Some minor planets have satellites.
   b. Meteoroids: billions exist. These are bodies smaller than a few hundred meters in diameter and
       are made of stone and/or metal.  Meteoroids are bodies that less tha 10 meters in diameter, otherwise it
      is a minor planet or asteroid.

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.
 

 
 
End of Chapter  2, Part I
Copyright 2005-2010 by R. J. Pfeiffer