-- Robert C. Victor
These orbit charts and accompanying data table can be used for plotting the positions of the six inner planets, and determining any planet’s visibility as seen from Earth. In addition to doing the problem set below as a desktop activity, students can “act out” each problem’s situation in the classroom, by having one student represent the Sun, another the Earth, and others the five other planets.
Be sure to have all students take a turn at representing the Earth. That student will do more than just stand in place, but will rotate as well, to determine planet visibility at dusk, in middle of night, and at dawn.
These two charts of the orbits of the planets, one showing Mercury through Mars, and the other Mercury through Saturn, depict the view as seen from the north side, or “above” the solar system. In these views, the direction of revolution of the planets about the Sun is counterclockwise. The outer circular scale is labeled with values of heliocentric longitude, measured from the Vernal Equinox, or apparent direction of the Sun as seen from
Earth at the beginning of northern hemisphere spring. That scale also indicates the directions of the thirteen zodiacal constellations (those in the plane of the
Earth’s orbit) from the Sun.
The directions of the five first magnitude stars Aldebaran, Pollux, Regulus, Spica, and
Antares, as well as the Pleiades star cluster, are also indicated. The outer circular scale should be imagined to be much larger than shown: Earth is one astronomical unit, or 8-
1/3 light minutes from the Sun, compared to stellar distances of many light-years. One light-year is approximately 63,000 astronomical units. On a chart where the
Sun-Earth distance (one a.u.) would be represented by one inch, a light year would be represented by one mile.
On both orbit charts, the Earth’s orbit is exactly in the plane of the sheet of paper.
For each of the other orbits, the portion drawn as a solid curve lies north of or above
Earth’s orbit plane. The dotted part of the orbit lies south of or below Earth’s orbit plane.
From the north side of the solar system, the
Earth’s rotation on its axis also appears counterclockwise. But the axis of Earth does not point at right angles to the plane of the orbit; rather, it tips away from the perpendicular, leaning by about 23.4° toward the top of the chart or the 90° mark on the circular scale.
Using both orbit charts and the data table, try working out the answers to these questions:
(1) Why is the Pleiades star cluster visible all night around November 20? Where (in what direction in the sky?) would you expect to see it at nightfall? In the middle of the night? At dawn’s first light? Why can’t you see the cluster for several weeks around May 20?
(2) On what approximate date each year is
Aldebaran visible all night? Give approximate date of all-night visibility for Pollux; Regulus;
Spica, Antares.
(3) On what approximate date each year is
Earth heading toward Antares and away from
Aldebaran? On that date, Antares is visible at
(dusk or dawn?) about 90 degrees from the
Sun, while Aldebaran is visible at (dusk or dawn?), also about 90 degrees from the Sun.
(4) In which month would a Last Quarter
Moon appear near the star Spica? Hint: The
Last Quarter Moon occurs when the Moon appears 90 degrees or a quarter-circle west
(clockwise in this top view) of the Sun.
(5) Which constellation is hidden on the far side of the Sun for about the first month of
Northern Hemisphere summer?

(6) Using the Inner Planets Chart, find which two planets will appear close together in our sky on Jan. 10, 2015? On Feb. 21, 2015? On
Apr. 22, 2015? For each pair, determine time of day it will be seen, at dusk or at dawn.
(7) Which planet will be at opposition, visible all night on February 6, 2015? In which constellation does it appear? Which bright star will appear about 11° east of that planet?
(8) In which constellation will the Full Moon appear on the night of April 3-4, 2015?
Which bright star will appear about 10° east of the Moon that night? As the Earth rotates on its axis, the star will appear to follow the
Moon across the sky that night. There will be a total eclipse of the Moon visible from western U.S. before dawn on April 4, as the
Moon passes through the Earth’s shadow.
(9) Which four planets will be visible at dusk
(soon after sunset) on April 22, 2015? List the four planets in order of their positions in the sky, from western horizon toward eastern horizon. As the Earth rotates, which two planets will set almost together, first and second? Which will set third? Last? Which bright planet not visible at dusk will rise later in the evening?
(10) Saturn will be at opposition, visible all night, about a week after the middle of what month in 2015? In which constellation will it appear? Which bright star will appear about
11° east of Saturn?
(11) Near the beginning of which month in
2015 will Venus reach its greatest angular separation from the Sun in the afternoon and evening sky? In what phase will Venus appear then? Observe it through a telescope in the daytime around then, and with telescopes and binoculars in following weeks.
(12) Which brilliant planets will form a very close pair on June 30, 2015? (Use Outer
Planets Chart.) When will the event be seen, at dusk or at dawn? The two planets will be easily seen within the same telescope field.
Describe their appearances.
(13) What alignment involving Sun, Venus, and Earth will occur on August 15, 2015?
Notice Venus will be located in the portion of its orbit plotted as a dotted curve, rather than solid. During the alignment on Aug. 15,
2015, will Venus pass north, or south, of the
Sun’s disk?
Before Aug. 15, 2015, the previous time
Venus passed between Earth and Sun occurred just over 19 months earlier, on Jan.
11, 2014. On that occasion, did Venus pass
north, or south, of the Sun’s disk? Just over
19 months before that, on June 5, 2012,
Venus passed directly in front of the Sun’s disk, causing a transit of Venus, which won’t happen again until December 10, 2117. From the orbit diagram, can you explain why transits of Venus can happen only in early
June or early December? During the weeks leading up to and following each of these
inferior conjunctions of Venus (June 5, 2012;
Jan. 11, 2014; and August 15, 2015), what will be the phase of Venus?
(14) Which two planets will appear within about one degree of each other on October 25 and 26, 2015? When will they be seen, in dusk or dawn? Which two other planets will be visible at the same time? Three of these four planets will fit within a 5° field, forming a trio, for eight days, Oct. 22-29, 2015.
(15) From late January through most of
February 2016, all five naked-eye planets will be simultaneously seen in twilight. On Feb. 1,
2016, the Moon will appear half full and close to one of the five planets. Plot all the planets’ positions for that date on the orbit diagrams, and determine: (a) When can you see all five planets, at dusk or at dawn? (b) Names of the planets in order of their apparent positions in the sky, from the eastern to the western horizon? (c) Name of the planet near the “half
Moon” on Feb. 1? (d) Rough dates in 2016 when each of the three outer planets will appear at opposition and be visible all night?
Robert C. Victor was Staff Astronomer at Abrams
Planetarium, Michigan State University. He now enjoys providing sky watching opportunities for

school children in and around Palm Springs.