ASTR 313, Majewski [FALL 2002]. Lecture Notes

## PLANETARY ASTRONOMY

REFERENCE: Kaler Chapter 11.

In this lecture, I will discuss observations of solar system objects other than the Sun and the Moon.

### A. PLACEMENT OF PLANETS IN THE SKY

ORBITAL PLANES

Most planets orbit very nearly in the same plane as does the Earth.

Thus, all planets will appear in the sky near the ecliptic plane, and wander through the constellations of the zodiac.

The orbital plane inclinations, and, therefore, the maximum distance each planet can be seen from the ecliptic, is shown in the figure below.

Note that Jupiter's moons and Saturn's rings also lie approximately in the plane of the ecliptic.

Just like with the Moon, a planet exhibits two orbital periods:

• A sidereal period which is the true orbital period with respect to the stars.

• A synodic period which is the apparent revolutionary period as seen from the (moving) Earth.

According to Kepler's Laws, the closer planets to the Sun have shorter periods and the planets farther out have longer periods.

• According to Kepler's Third Law, the period of a planet, P (in Earth years) is related to the radius of its orbit, R (in Earth orbit radii) by:

P2=R3

SOME COMMON TERMS IN PLANETARY OBSERVING

A number of terms are used in discussing how different objects in the solar system appear are configured and appear in the sky with respect to one another.

INFERIOR AND SUPERIOR PLANETS

Planets can be categorized based on the size of their orbits, which determines where and how they can be seen in the sky:

• Inferior Planets (Mercury, Venus) orbit inside the Earth's orbit.

• Therefore, inferior planets always appear near the Sun.

• Elongation is the angle between inferior planet and Sun. Greatest elongation is the largest angle between an inferior planet and the Sun.

Greatest elongation of Mercury is 28o.

Greatest elongation of Venus is 47o.

• Thus, to see these planets, one must wait until the Sun is just below the horizon (to block its glare), but not too far or the planet itself will have also set.

• Depending on whether the planet is East or West of the Sun in its orbit, the inferior planet will be either a "morning star" or an "evening star".

• On some occasions, an inferior planet will be in the same direction as the Sun, in conjunction. Inferior planets have two kinds of conjunctions:

• Inferior conjunction, when the planet is between the Earth and Sun. Only inferior planets can do this!

• Superior conjunction, when the planet is on the other side of the Sun.

• Of course, depending on where the object is in its orbit around the Sun, an inferior planet will show phases, like the Moon.

As the following images of Venus show, it's phases and its size change dramatically depending on where it is in its orbit around the Sun.

• On rarer occasions (requiring an Earth-Sun-planet syzygy -- both the Earth and the planet to be near the line of nodes where the planet's orbital plane intersects the Earth's orbital plane), a planet will be completely occulted by the Sun (at superior conjunction), or the planet can transit the Sun (at inferior conjunction).

• Earth is near the Mercurian line of nodes around November 11 and May 9 of each year.

• The next time Mercury will be at inferior conjunction on these dates (allowing a transit) is in May 2003 and November 2006.

##### The beginning ("ingress") of a transit of Mercury. This is an image of the transit of Mercury as seen by the TRACE satellite in November 1999. Mercury passes the Earth every 116 days, but, because of Mercury's 7o orbital tilt, only one out of 23 Mercury orbits results in a transit of the Sun as viewed from Earth. Click here to find a movie version of the transit.

• Venusian transits are much rarer. The Earth is near the Venusian line of nodes around June 8 and December 9.
• The next time that Venus will be at inferior conjunction at this point in its orbit and allowing a transit across the Sun will be June 8, 2004 and June 6, 2012.

• But the last time it happened was 1882!

• Only five Venus transits have ever been observed by humans!

##### Stamp commemorating the 1768 transit of Venus as seen by Captain Cook. Click here for a page from Cook's Polynesian expedition where he drew images of Venus as it approached the Sun's limb (the engraving also shows some botanical and zoological specimens).

• Superior Planets (e.g., Mars, Jupiter, Saturn, ...) orbit inside the Earth's orbit.

• Unlike inferior planets, superior planets can have any angle with respect to the Sun. Certain angles have special names:

• Opposition is when the planet is opposite the Sun in the sky (i.e., an elongation of 180o).

• Quadrature is when the planet is 90o from the Sun.

• Like inferior planets, superior planets can be in conjunction with the Sun (i.e., an elongation of 0o). But only superior conjunctions are possible of course, so we simply say "conjunction" for superior planets because a superior conjunction is understood.

• THOUGHT PROBLEM: Are solar transits possible with superior planets?

• THOUGHT PROBLEM: When does a planet in opposition transit your meridian? A planet in conjunction? Quadrature?

• Superior planets also cannot show phases -- their fully illuminated side is always facing the Earth!

• However, superior planets (but not inferior planets) exhibit something called retrograde motion.

• Planetary motions (seen over nights or months of time -- depending on the planets distance from us) are generally eastward in the sky.

• However, as is shown in the image below, occasionally superior planets will stop moving eastward with respect to the stars, and for a period will move westward before turning around and continuing to move the normal easterly direction.

##### Image made as a time exposure of a planetarium simulation of planetary orbital motions as seen from Earth. Note the retrograde loops.

• Note, retrograde motion is not real backwards motion by the planets!

• The retrograde loops are an illusion caused by the superposed effects of the motion of the Earth, as demonstrated in the image below.

##### The image shows the position of the Earth and Mars at 11 successive time steps. Because the Earth is in a smaller orbit, by Kepler's Laws it moves faster in its orbit, and it overtakes/passes Mars near opposition. The perspective of Mars against the background "fixed stars" as seen from the Earth shows a retrograde motion during the opposition.

• The following flash movie demonstrates what happens when we see retrograde motion in Mars.

• The following flash movie demonstrates what the retrograde motion in Mars looks like from the Earth perspective.

### B. OBSERVING PLANETS

SIZE AND BRIGHTNESS

Note that the brightness of planets vary:

• Our distance from the planet changes.

• Their distance from the Sun changes (slightly, due to elliptical orbits).

• Inferior planets have phases.

• The ecliptic has varying altitudes above the horizon, so there is more or less extinction from the Earth's atmosphere.

With the 8-inch night lab telescopes, you can easily observe all of the planets except Pluto.

• Pluto is 15th magnitude. The next faintest planet is Neptune at only 7.8 magnitude.

• The brightest planets -- Mercury, Venus, Jupiter, Saturn -- can be observed in daylight.

And the size of planets vary:

• Because our distance from the planet changes.

THOUGHT PROBLEMS:

• When would a superior planet be brightest? Biggest?

• Is the brightest time of an inferior planet as easy to figure out?

• When is an inferior planet largest?

One may notice that when observed with the naked eye, planets do not twinkle as much as stars do.

• Recall that twinkling, or scintillation, has to do with constantly changing refraction by rapidly moving pockets of different density air in the Earth's atmosphere and along the line of sight.

• On a typical night, the size of a seeing cell, a pocket of air at about the same density and refracting light similarly, is of order 10 cm across, and many kilometers up. The angular size of the seeing cells is tens of arcseconds -- much larger than the size of a star, which is greatly affected by each cell that passes through the line of sight.

• The reduced scintillation for planets has to do with the angular sizes of the planets compared to the angular sizes of stars and the typical seeing cell.

• Of course, in reality stars are actually much bigger than stars, but stars are so far away that their angular sizes are tiny fractions of an arcsecond.

• Since planets can have angular sizes covering many seeing cells at once, the differential refractive effects of the individual cells is averaged out and has much less effect on the brightness of the disk of the planet.

• Of course, through a small telescope you can see the surface features of a large planet like Mars, Jupiter or Saturn appear to churn and smear out in different parts of the image disk at different times -- in this case you are resolving the effects of the different seeing cells.

• Under extremely turbulent atmospheric conditions, even planets will "twinkle".

Galilean Moons of Jupiter

• Only the four moons of Jupiter discovered by Galileo (Io, Europa, Ganymede, Callisto) are relatively easy to see with a small telescope.

• To remember the Galilean satellites in order of distance from Jupiter, just remember the mnemonic "I Eat Green Carrots".

• These Galilean moons have relatively rapid orbital motions around Jupiter and can be readily tracked.

• NASA's Voyager and Galileo missions revealed astonishing differences in surface constitution among the four, but through small telescopes, unfortunately, no surface details are apparent.

• This "mini-solar system" shows interesting eclipses by the planet, occultations by the planet, transits across the face of Jupiter, and shadow casting on the planet as the moons quickly orbit around the gas giant.

• Using these phenomena, the speed of light was first measured by the Danish astronomer Ole Roemer in 1670. His experiment can be repeated by you in optional Lab 11 (described below).

Venus phases diagram from http://www.physics.ucla.edu/~huffman. Venus phases photo sequence from http://zebu.uoregon.edu/~imamura/121/images/. All other material copyright © 2002 Steven R. Majewski. All rights reserved. These notes are intended for the private, noncommercial use of students enrolled in Astronomy 313 at the University of Virginia.