### Overview

Students model the planets in their actual positions around the Sun, incorporate the geometry of viewing parameters from Earth and visualize where planets will be seen (if visible) in the night sky on any given date.

### Management

Make a 360-degree calibrated scale. Image credit: NASA/JPL-Caltech | + Expand image

Insert the model Sun into the center of the calibrated scale. Image credit: NASA/JPL-Caltech | + Expand image

Make a loop at one end of the length of string representing the scale distance to each planet and attach a bead representing the planet to the other end of the string. Image credit: NASA/JPL-Caltech | + Expand image

Wrap the string around pieces of cardboard for easy storage. Image credit: NASA/JPL-Caltech | + Expand image

• Well in advance of conducting the lesson with students, build a 360-degree calibrated scale with a vertical shaft in the center.

1. Use the protractor and felt-tip permanent marker to mark and label every 5 degrees along the circumference of the wood.
2. Insert the wood dowel into the pre-drilled hole in the center of the circular piece of wood or particleboard.
3. For additional effect, place the wood sphere or blank wooden doll head on top of the dowel to represent the Sun. Paint it yellow, if desired.
• Select an outdoor (or very large indoor) location where a large-scale model of the solar system will fit. Determine the scale of your model based on the longest distance available in the space. For best results, create a scale model that is at least as large as 1 au = 150 cm. A larger model is better for visualizing the planets in the sky. A smaller model will fit better in a smaller space but the inner planets will be too crowded for proper effect.
• Compute the distances to the planets you plan to have students represent with the model. It may be practical to only represent planets that are visible to the unaided eye (up to and including Saturn). Remember that the Sun will be in the middle of your model and planets might be on opposite sides of the Sun.
• Cut strings to the length corresponding with each planet’s average scaled distance from the Sun, adding enough length to create a loop at one end that will fit over the model Sun and tie a wooden bead on the other end.

• Color-coding or otherwise labeling the strings and beads can be helpful in organization.
• For ease of storage, wrap each string around a scrap piece of cardboard labeled with the planet’s name. Alternately, students can work together to cut and tie strings to beads as the first step in the lesson.
• This lesson is most powerful when delivered at a time of year when more than one planet will be visible in the night sky. If you have flexibility on when to deliver this lesson, consider sketching out the radial model for various times of the school year and picking the time that has the most planets visible at night and/or the highest probability of clear skies for viewing.
• If students live in a city with a lot of light pollution, consider doing this activity at a time of year that one of the brightest planets, Venus or Jupiter, will be visible at night.

### Background

Many images and scale models of the Solar System represent all the planets in a straight line extending from the Sun. Of course, this isn’t an accurate representation of planets’ positions, as planets orbit the Sun at different rates and can appear at various locations around the Sun.

How big are the planets and how far away are they compared to each other? See how the sizes of planets and the distances between them compare in this video. Credit: NASA/JPL-Caltech | Watch on YouTube

We know the orbits and orbital rates of the planets in our solar system, so we can predict the positions of the planets around the Sun on any given day. These positions can be referenced using a Sun-centered, or heliocentric, longitude system. Heliocentric longitudes are one aspect of an ecliptic coordinate system. The next paragraphs explain the details of this coordinate system. Interest in these details might vary by instructor. A thorough understanding of these details is not necessary for successful lesson delivery.

An ecliptic coordinate system is used for identifying the positions and orbits of objects in the solar system, much the same as lines of longitude and latitude are used to denote the locations of places on Earth.

A zero point for heliocentric longitudes and latitudes must be defined for reference, just as on Earth, where zero degrees latitude is located at the equator and zero degrees longitude is located at Greenwich, England. Zero degrees heliocentric latitude is located on the ecliptic plane – the plane defined by Earth’s movement around the Sun. Zero degrees heliocentric longitude is located at the vernal equinox. The vernal equinox is one of two places on the imaginary celestial sphere where the ecliptic plane intersects the celestial equator, or the projection of Earth's equator into space.

The center of planetary motion is measured from the barycenter, or center of mass, of the solar system, which is very close to the center of the Sun. For practical purposes in this activity, we use the Sun as the center of the heliocentric model.

It is important to note that most celestial motion is counterclockwise as viewed from above. All the planets in the solar system move around the Sun in this manner.

The heliocentric longitude of a planet is the angle, measured in degrees, between the vernal equinox and the planet as seen from the Sun. (In this model, the vernal equinox is an established zero-degrees location on a circular protractor.) It is measured on the ecliptic plane in the orbital direction of the planet, which is counterclockwise as viewed from above.

Knowing the heliocentric longitudes of the planets on a given date and the relative distances of the planets from the Sun, students can create a realistic radial, or circular, model of the Solar System. This model can be used to understand which planets will be visible in the night sky, and when and where they will be visible, as well as why we are unable to see other planets on a given date.

As with most models, this model of the Solar System contains some simplifications for demonstration purposes. As mentioned above, the planets orbit the barycenter, or center of mass, of the solar system, which is a constantly changing location based on the positions of the planets. This model shows the Sun as the center of planetary orbits for simplicity. Additionally, planets orbit the Sun in elliptical paths, not circular paths. In this model, each planet’s orbit is represented as a circle, though some planets and dwarf planets actually have rather eccentric orbits. The radii of the strings in this model represent the average distance between each planet and the Sun. Also, in this model, the planets are all represented on the same plane.

In reality, orbital inclination varies, with some planets and dwarf planets being several degrees out of plane. For example, the orbital inclination of Mercury is 7 degrees, while the orbital inclination of Ceres is 11 degrees, Pluto is 17 degrees, Haumea is 28 degrees, Makemake is 29 degrees and Eris is a whopping 47 degrees.

### Procedures

#### Making the model

1. If you have not already done so, have students cut strings to represent each planet’s average scaled distance from the Sun. The strings should be long enough that students have space to make a loop on one end of the string that will fit over the model Sun and, on the other end, tie on a wood bead representing a planet. Consider color-coding the strings and beads.
2. If strings are already cut, unwind them from their cardboard keepers and have students work as a group to lay them out and determine which string represents which planet. Shorter strings can be easily handled by one student, but longer strings for the outer planets will need at least two students to manage. Note that the beads, being all the same size, are not representative of scale sizes of the planets.
3. Insert the dowel and model Sun into the center of the calibrated circular scale and explain the concept of heliocentric longitudes. Explain that the class will be creating a realistic model of the solar system as it appears right now, with planets at a scale distance in their proper locations around the Sun.
4. Place the scale on the ground, oriented so that the heliocentric longitude of the most distant planet you’ll be representing points toward a long open space.
5. Hand out copies of the heliocentric longitude chart for the current year.
6. Appoint a “Sun Keeper” to hold the central shaft representing the Sun steady as the various strings are placed, and to assist with accurate placement.
7. Ask for a student volunteer to represent Mercury. Have them retrieve the string for Mercury.
8. Ask the class to tell the student representing Mercury the heliocentric longitude of Mercury for the current date. If the current date is not noted on the heliocentric longitude chart, pick the date on the chart that is closest to the current date.
9. Have the student place the loop of the string over the Sun, locate the heliocentric longitude on the circular scale and fully extend Mercury’s string along the ground so that it crosses the appropriate longitude on the scale. Have the student place the bead representing the planet on the ground.
10. Repeat steps 7-9 for the remaining planets so the entire radial model of the solar system in its current state is represented on the floor.
11. A student places the loop of the string over the model Sun. Image credit: NASA/JPL-Caltech | + Expand image

#### Modeling Earth’s rotation and revolution

1. Ask the student who represented Earth to stand over the wooden bead representing Earth. Explain to the class that they will be telling the Earth student what to do in response to the questions you ask.
2. A student stands over the wooden bead representing Earth. Note: Strings in the model have been highlighted for visibility. Image credit: NASA/JPL-Caltech | + Expand image

3. Ask the class which way Earth revolves around the Sun. Answer: counterclockwise as viewed from above.
4. Have Earth walk one complete revolution around the Sun. Ask students what unit of time this action represents. Answer: One year.
5. Ask students what Earth should do to represent one day. Answer: Turn in place, one entire turn, in a counterclockwise direction (as viewed from above).
6. Designate the nose of the Earth student as your town. Ask the class which way Earth should face to represent daytime in your town. Answer: Earth should face toward the model Sun. Have the Earth student position themselves so that their nose represents daytime in your town.
7. The Earth student should face the model Sun to represent daytime. Note: Strings in the model have been highlighted for visibility. Image credit: NASA/JPL-Caltech | + Expand image

8. Ask the class what time it is when Earth is standing with the Sun directly in front of their nose. Answer: Noon.
9. Ask students which way Earth should face to represent nighttime in your town. Answer: Earth should turn their back to the Sun. Have the Earth student position themselves so that their nose represents nighttime in your town. Be sure they are rotating in a counterclockwise direction.
10. The Earth student should turn their back to the model Sun to represent nighttime. Note: Strings in the model have been highlighted for visibility. Image credit: NASA/JPL-Caltech | + Expand image

11. Ask the class what time it is when Earth is standing with the Sun directly behind their back. Answer: Midnight.
12. Ask the class what other times of day can be represented by the Earth student. Answer: Any time.
13. Ask the Earth student to stick their arms out straight, perpendicular to the sides of their body. Explain (or ask students to deduce) that the Earth student’s left and right arms represent the horizon. Have the Earth student look left and right and imagine they are looking from horizon to horizon, east to west.
14. The Earth student should stick their arms out straight to represent the horizon. Note: Strings in the model have been highlighted for visibility. Image credit: NASA/JPL-Caltech | + Expand image

15. Ask the class to determine which arm represents the eastern horizon and the western horizon. Answer: Left is east, right is west.
16. Ask the class to direct the Earth student to represent sunrise for their town. Answer: The Earth student should stand, arms out, with their left arm (east) pointing directly at the model Sun.
17. The Earth student should point their left arm toward the model Sun to represent sunrise. Note: Strings in the model have been highlighted for visibility. Image credit: NASA/JPL-Caltech | + Expand image

18. Ask students to identify the approximate time this position represents for their town (Earth’s nose). Answer: 6 a.m., or whatever time of day the Sun rises in the morning.
19. Ask the class to direct the Earth student to represent sunset for their town and say what time of day this represents. Answer: The Earth student should stand, arms out, with their right arm (west) pointing directly at the model Sun. The time of day is approximately 6 p.m., or whatever time the Sun sets in the evening. Be sure the Earth student is turning on their axis in a counterclockwise direction (as viewed from above) for all orientation changes.
20. The Earth student should point their right arm toward the model Sun to represent sunset. Note: Strings in the model have been highlighted for visibility. Image credit: NASA/JPL-Caltech | + Expand image

#### Visualizing planets in the sky

1. Have the Earth student, while standing in the sunset position, hold both arms out to represent the horizon. Ask them what planets they can see in the “sky,” displayed on the visible ground between their outstretched arms. The planets easiest to see with the unaided eye are Venus, Mars, Jupiter and Saturn. If any of these planets are in the model “sky,” the same planets will be visible in an analogous actual sky position tonight near sunset.
2. Have the class instruct the Earth student to position themselves to represent 9 p.m., when the sky will be darker. Have the Earth student point out the planets that will be visible tonight at approximately 9 p.m. Have the Earth student point to the approximate location in the sky where each planet will be visible tonight.
3. Have the class instruct the Earth student to position themselves to represent various other times of the night, including just before sunrise, and identify the planets that will be visible at those times.
4. Have the class, with the help of the Earth student, explain which planets are not visible at night right now and why. Answer: Some planets will be “up” during the day and the light of the Sun will obscure observation.
5. Have students “time travel” by advancing the planets in the model to a time in the future, for example, next month, and then next year, if heliocentric longitudes are available. Have students observe that over the same period of time, planets closer to the Sun advance farther in their orbit than planets a longer distance from the Sun. Have students draw conclusions or offer explanations for this to the best of their abilities. Most students will be able to correctly conclude that the inner planets are moving faster than the outer planets. More advanced students may be able to make the connection to Kepler’s third law.
6. Have the class, with the help of the Earth student, explain why Mercury is difficult to see no matter where it is in its orbit. Answer: It will always be low on the horizon and, thus, close to the Sun in the sky. The brightness of the Sun, even after sunset, will often obscure our view of Mercury.
7. Have students take turns being “Earth” so they can go through the motions and see firsthand which planets will be visible tonight and why.
8. Have students explain why Venus is sometimes visible in the morning and sometimes visible in the evening. Note that Venus is commonly referred to as the “morning star” or “evening star,” but it is not a star at all.
9. Instruct the students to look at the sky tonight (or in the early morning) at home and try to locate the planets that they now know are visible. Remind students of the expected positions of the planets. Instruct students to face south for the proper frame of reference.
10. Tomorrow, ask students to report what planets they were able to see last night and approximately where they appeared in the sky. Note: If students live in a city with a lot of light pollution, they may not be able to see all the planets that are in their line of sight. However, Venus and Jupiter are so bright that they can even be seen from Downtown Los Angeles.

### Assessment

• Ask students to determine which planets will be visible on a given date.
• Ask students to identify where those planets will be in the night sky and at approximately what time.