There is something about the navigational planets that makes them special. Perhaps it is because they are personified by their Roman names – Mars, the god of war; Venus, the goddess of love. The Arabic-based names for the stars don’t possess quite the same ring. The relative proximity of the planets must have something to do with it, tooandmdash;the stars are unimaginably far, but the planets strike one as fellow voyagers, like the lights of a distant ship on a dark ocean.
In addition to their romantic allure, the navigational planets have real benefits for the celestial navigator: They usually add one or two to the number of celestial bodies available at either morning or evening twilight. In order to shoot them, however, a navigator has to be able to find them. But, unlike stellar constellations, there is no way to memorize the positions of the planets; they are always on the move.
The planets’ wandering across the field of fixed stars undoubtedly inclines the navigator towards wonder: How is it that brilliant Venus never lies along one’s meridian at midnight? Why is Mars sometimes available at both morning and evening twilight? How can a giant like Jupiter seem to stop and slide backwards across the field of stars?
Planetary motion has always intrigued astronomers and navigators. The ancient Greeks noted that certain bodies appeared to roam the night sky and dubbed these objects planetes – Greek for wanderer.
The wanderings these ancient astronomers noted, and the ones we can observe, involved the apparent motion of the planets. That is, the motion as observed from the moving platform of the Earth. From this apparent motion, early astronomers then attempted to discern the true motion of the planets (and also the sun, moon, and stars). They were hampered in this task by an understandable, if erroneous, underlying assumption: that Earth was the center of the universe. As astronomy advanced and more observational data accumulated on planetary motion, this became and increasing untenable position. In order to adequately explain the observed motions, ancient astronomers had to devise complex orbits for the planets that included large circles called deferents and small circles called epicycles.
The scheme of a heliocentric, or sun-based, solar system put forward by Nicholas Copernicus in the sixteenth century removed the need for deferents and epicycles. Later, Johannes Kepler cast aside the last element of classical astronomy by stating that planetary orbits were not circularandmdash;considered a perfect shape by ancient astronomers and the only viable choice for the orbit of a heavenly bodyandmdash;but instead, were elliptical in shape.
Thus, we get the following scheme for the solar system: Mercury and Venus inside Earth’s orbit, with Mars, Jupiter, Saturn, Uranus, Neptune and Pluto outside the orbit of Earth, and, of course, the sun at the center. The location of the planets relative to Earth becomes a useful method for classifying them: Mercury and Venus, are “inferior” planets, while the others are “superior” bodies. Not only do the terms inferior and superior tell us something about the relationship of a planet to Earth, they also give us a general idea of how a planet will move in the sky.Inferior planets
There is certainly nothing substandard about Mercury and Venus. In fact, they have some excellent qualities. However, they are closer to the sun than Earth and that classifies them as inferior planets.
Since they are closer to the sun, they have a shorter path to follow and their periods of revolution are less than Earth. While it takes Earth roughly 365 days to complete one sidereal year (this is the time required for a planet to go around the sun and return to its starting position as measured against the background stars), Mercury does the circuit in a mere 88 days. Venus, meanwhile, revolves in 225 days, or 62% of an Earth year.
If Earth were stationary, Venus and Earth would have a close approach every 225 days. Earth, however, is also moving. If we factor in Earth’s motion, then every 584 days, the two planets will have their closest approach. This period between the close approach of any planet to Earth is called a synodic year. Mercury has short synodic period of 116 days, it easily catches and overtakes the slower Earth. However, since Earth’s and Venus’s periods of revolution are closer, Venus has a longer synodic period than Mercury. We’ll see what this means in a minute, but first we need to look at the orbital geometry of the inferior planets.
When a planet lines up with the sun, as seen from Earth, the result is called a conjunction. We can see by referring to figure X that inferior planets experience conjunction twice each synodic period: When the planet is on the far side of the sun, we call it andquot;superior conjunction;andquot; whereas, when a planet is on the same side of the sun as Earth, the term is andquot;inferior conjunction.andquot;
Of course, even a quick glance at figure X reveals something important about the inferior planets: in order to see Mercury or Venus, we have to look toward the sun. And when the sun is above the horizon, it does a very good job of blotting out the reflected light of Mercury and Venus. (It is possible to precalculate the position of Venus and shoot it during the day, but that’s a somewhat advanced technique that we’ll leave to another article.) Therefore, due to the overbearing effect of the sun, we won’t see Venus or Mercury at either superior or inferior conjunction. In fact, we’ll only see these two planets when the sun is out of the picture: either after the sun sinks below the horizon, or before it makes an appearance at sunrise.Elongation
The length of time either of these planets is visible depends on something called elongation – a measure of the angular difference between the sun and the planet as seen from Earth. This angle is shown in figure X. A line drawn from Earth that is tangent to an inferior planet’s orbit will describe that planet’s farthest easterly or westerly elongation. Mercury’s largest elongation is 27 degrees, while Venus reaches a point 46 degrees away from the sun.
By looking in the arc to time conversion table in the Nautical Almanac, we can convert the 27 degree elongation of Mercury into a time of one hour and 48 minutes. This means when Mercury is at farthest westerly elongation, it will be visible above the horizon for more than an hour before the sun rises. Roughly the same window is available when Mercury is at greatest easterly elongation. Then why isn’t Mercury considered one of the navigational planets? To answer this, we need only remember fleet-footed Mercury’s short synodic period. From a starting point at inferior conjunction, Mercury reaches westerly elongation, passes behind the sun and hits superior conjunction, achieves easterly elongation, and then moves into inferior conjunctionandmdash;all in roughly 116 days. Because this period is so short, Mercury spends about half its time lost in the sun’s glare as it shuttles between easterly and westerly elongation. (On the other hand, for a few days around greatest elongation, Mercury makes a viable sextant target. Maybe the Nautical Almanac office could publish a supplement giving Mercury’s GHA and declination for those days.)
Compared to Mercury, Venus’s motion seems almost stately. Where Mercury gets lost in the bright lights seven times in 1993, Venus is only drowned out by the sun twice. The main reason for this lucky fact lies in the relative speeds of the two planets. Venus, with its larger orbit, has a longer revolutionary period than Mercury – about 225 days. This compares with 365 days for the period of our observation platform (Earth). The difference between these speeds is less than that between Mercury and Earth. Or, in other words, even though Venus is faster than Earth and eventually laps us, we are able to keep her in our sights for a longer period than we can with overstimulated Mercury.
The relatively small difference between the sister planets (Earth and Venus are similar in size and density), gives Venus a synodic period of 584 days, five times that of Mercury; more than a year and a half elapses from one Venusian inferior conjunction to the next. This means that Venus hangs around for a while as either an evening or morning planet. Navigators have every reason to be happy about this since Venus is usually quite bright, making it a good sextant target. (Venus’s great brightness stems both from the fact that it makes the closest approach to Earth of any planet, and due to its clouds, which are highly reflective of sunlight. For example, the airless moon, quite bright when full, is actually far less reflective than the cloud-swaddled Earth. Another factor affecting the magnitude of Venus is the position of the planet in its orbit. Just like the moon, Venus actually goes through phases, see figure X. Even though a navigator can’t see the phase, the change in magnitude is observable.)
This year, Venus achieves greatest easterly elongation in mid-January. The planet’s greatest westerly elongation occurs in the middle of June when it rises in the morning about three hours before the sun. Venus remains a morning body from early April to late Novemberandmdash;a large chunk of the year.
So, Mercury and Venus are always tied to the sun, Mercury so much so that we rarely ever see it, let alone put a sextant ‘scope on it. A few hours after sunset, an observer on Earth finds himself within the dark hemisphere; shielded from the sun’s mighty lamp, he now sees the cold reaches of the solar system outside Earth’s orbit. Mercury and Venus will have slipped below the horizon, and, by the time of local midnight, will be on the far side of Earth. Up in the sky there will most likely be other planets: Mars, Jupiter, Saturn, and, if our observer has a powerful telescope and some patience, the dim light from Uranus, Neptune and frozen Pluto. Because the outer three are so dim, they can’t be shot with a sextant. The closer three, however, make excellent celestial targets.Superior planets
Mars, Jupiter and Saturn are called superior planets since their orbits are outside Earth’s orbit. The anchor points of a superior planet’s orbit are a bit different from those of an inferior planet. For example, when Mars is abreast of, and closest to, Earth, it is at opposition. The red planet then proceeds on to west quadrature, then to conjunction, next to east quadrature, and finally back to opposition. This scheme, of course, results from the combination of Earth’s motion and the motion of Mars, or of any other superior planet. While the inferior planets speed past the slower Earth, now the situation is reversed: Earth is the fast mover, turning inside the superior planets.
Mars, closest of the three, has an orbital period of 687 days, or 1.88 times the period of Earth. One might think that Earth could easily whip past Mars, but, actually, Mars has a synodic period of about 780 days, a little more than two years. It takes about 26 months for Mars to go from one opposition to the next. For example, Mars was at opposition in late November of 1990. Almost a year laterandmdash;early November, 1991andmdash;it was at conjunction and lost in the sun’s glare. By January 7 of this year, we had again caught up to the red planet and it was at opposition.
When a superior planet is at opposition, its GHA differs with that of the sun by 180 degrees. This means that it will rise in the east at sunset, cross one’s meridian at midnight, and set in the west at sunrise. This all-night availability often means that at opposition, a superior planet can be used at both evening and morning twilight. We will also have advantage of seeing one full hemisphere of the planet illuminated (it has a phase of “full”). This fact, allied the planet’s relative proximity, will cause it to shine brightly. Mars, at opposition in January, had a magnitude of -1.4, while in September, as it heads for conjunction, its magnitude will dim to +1.6 (the larger the negative number, the brighter the object).
While we have to wait roughly two years to get Mars at opposition, Jupiter and Saturn are much more cooperative. Jupiter has a revolutionary period of 11.86 years. Obviously, at that rate Earth can easily lap this proto-star. (Had Jupiter been a bit bigger, it would have produced sufficient pressure at its core to ignite the fires of nuclear fusion and we would have a two-star solar system, but that’s another story.) In the time it takes Earth to fly through one circuit of the sun, Jupiter will only have inched through 8% of its orbit. With so little movement on the part of Jupiter, its easy to see that the synodic period of Jupiter should be fairly close to a year. In fact, it is about 399 days. Saturn, which requires 29.5 years to get around the sun, has an even shorter synodic period: 378 days. So, both these planets can be seen at opposition roughly every 13 months. For 1993, Jupiter reached opposition in early April, while Saturn is scheduled for late August. Retrograde motion
When discussing the motion of any planet as observed from Earth, we’re dealing with combined motion: the movement of Earth relative to the motion of the planet. And because no two planets are revolving around the sun in lock step, planets will pass each other. This passing produces a relative motion effect called retrograde motion. This was observed by the ancients and was another tip-off that planets were different from stars.
When a planet goes retrograde, it appears to move andquot;backwardsandquot; against the field of stars. To understand how this works, we first have to look at how the stars move.
Looking down on Earth’s orbit from above the North Pole, our planet spins counterclockwise as it heads counterclockwise around the sun. Thus, with each rotation around its axis, Earth has also moved forward in its orbit. This causes any star to appear to rise four minutes earlier each day. In other words, a star that is on the eastern horizon at midnight on the first of the month will, a few months later, be close to an observer’s meridian at midnight. The star will appear to have slid to the west with each passing night.
In celestial navigation, we think of all the stars as being sprinkled around on the inside a great globe encompassing Earth called the celestial sphere. Thus, the celestial sphere appears to ratchet to the west each night. (On any one night, of course, the sphere will appear to smoothly rotate from east to west. However, but if we could take out that nightly motion, we would see the stars jump one degree to the west each succeeding night.)
One of the givens of celestial navigation is that the sun moves through 15anddeg; of arc in one hour, so naturally, we might think that all celestial bodies do the same. Actually, the stars move a little more: 15anddeg; 02.5′ every hour. On the other hand, if we look at only the hourly values of GHA for the planets, sometimes they move greater than 15 degrees, sometimes less than that amount. There is an additional correction to the GHA of a planet called the v correction. This correction tells us the degree to which a planet’s motion is deviating from the 15 degree value.
Let’s take October 10, for example. On that day, the v factor for Saturn is 2.5. This means that Saturn moved 15anddeg; 02.5′ every hour. Clearly then, Saturn is moving at the same pace as the stars and would appear to be motionless against the starry background. What about Mars? It has a v factor of 0.8. Over the course of an hour, Mars moved only 15anddeg; 00.8′. So, it was not keeping up with the stars, but was falling behind 1.7′ each hour. The result of this is an apparent motion not to the west, but to the east, relative to the background stars. And look at Venus, it had a v factor of -0.4, or an hourly change in GHA of 14 degrees 59.6′. This shows up as a 2.9′ hourly slide to the east.
What we’ve found here is called the direct motion of the planets. That is, from Earth, the planets seem to spend most of their time moving eastward against the stars. When Venus catches up with Earth, or when Earth catches up with a superior planet, however, the stage is set for retrograde motion.
Imagine that we are riding a bicycle in an empty parking lot and we are joined by a child on her favorite trike. We decide to ride around in a big circle so we can keep an eye on the youngster. Our young friend likes this idea and copies us by riding in a larger circle outside of ours, at a much slower speed (tricycles only go so fast, after all). When we are the far side of our circle, we’ll see our friend happily plugging forward. As we make our closest approach to her, we’ll see her seem to slow down, stop, and then appear to move backwards relative to the background. Then, after we have passed her, she will again appear to move forward in her circle relative to the background. She, of course, has never deviated from moving forward at a steady pace, but to us, she seems to have gone through short bit of “backwards” or retrograde motion (see figure X).
We can see the that the planets also will undergo retrograde motion whenever their v factor is greater than 2.5′ Remember that retrograde motion takes place when we are about to be passed or are passing another planet. We saw earlier that Mars reached opposition on January 7 of this year. On January 4th, Mars had a v factor of 3.6, and was moving 15 degrees, 03.8′ every hour. This was 1.3′ more than the stars, so Mars appeared to be sliding westward relative to the stars. It was in the throes of retrograde motion.Loops in the sky
Since the planets are not all on the plane of the ecliptic, but are inclined at various angle to it (Venus 3.5 degrees, Mars 1.85 degrees, Jupiter 1.3 degrees, Saturn 2.5 degrees), not only do they stop and move westward when retrograde, they also change their declination. Because of this, they appear to trace small loops against the stars. To ancient astronomers, these loops were a real challenge to their view of an Earth-centered universe. In order to explain them, they were forced to invent the deferents and epicycles mentioned earlier. The result was a system far more intricate than reality. (This points up the dictum put forth by the 14th century English scholar William of Occam, known as Occam’s razor: The simplest explanation is the best.)
Now that we have described the motions of the planets and have a general idea of how they move, how do we find their exact positions at the time of twilight?
There a few methods for doing this. One very effective method is to use a device called the Rude Starfinder (2102-D). This tool consists of a flat, circular base plate and a series of transparent templates. True to its name, it can be used to find the position of any navigational star. However, it can also reveal the positions of the moon or any of the planets.
The first step in using the starfinder for planets to calculate something astronomers call Right Ascension (RA). This is the angle measured from Aries eastward to the bodyandmdash;the opposite of Sidereal Hour Angle (SHA) which is measured from Aries westward to the body. In other words, to calculate the RA of a planet, one can simply subtract the planet’s SHA from 360anddeg; and the result will be RA. The SHAs of the planets are listed below the star list on the daily pages of the Nautical Almanac. While we are there, we need to pick up the planet’s whole degree of declination from the daily page.
Armed with the RA and dec., we pop the red template onto the starfinder’s baseplate. Ignoring all the other numbers around the outside edge of the red template we just use the zero mark. Reading the scale on the outer edge of the baseplate, we line up the zero mark with the number of the planet’s RA. Then, in the cut out window, we make a pencil mark using the vertical scale along the edge of the window, either north or south depending on the declination of the planet. We can take the red template off and draw the symbol for that planet where we made our mark.
After we have marked the positions of the four planets, we can take the red template off the base plate and pop on the blue template that is closest to our DR latitude. After lining up the arrow on the blue template with the value of LHA Aries for the time of twilight, we can then find the azimuth and altitude for each of the planets.
It is also possible to use the planet diagram in the Nautical Almanac for getting a good idea of planetary positions (see “Eyeball precalculation,” Issue No. 38). The facing page across from the diagram gives helpful information about how to spot the planets and documents those times when it might be easy to mistake two nearby planets for each other.
The most enjoyable method for determining planetary positions is to spend time under the starry vault. Look around the sky and discover where the planets are located. If one knows the constellations, one can quickly get a feeling for the planets because a familiar group of stars will be joined by a stranger and the bright interloper will be one of the planets. Go out a few nights and a few mornings before leaving on a voyage. Not only can one get a feeling for the planets, but one can also figure out what navigational stars will be available during the trip.