Scale Model

WANDER: THE CONCORD, NH SCALE MODEL OF THE PLANETS

Thousands of years ago our ancestors searched the night sky. They saw that while almost all the stars stayed fixed in the same position relative to each other, five of them were always moving. These five wandering stars were accompanied by two other obvious celestial moving objects- the Sun and the Moon. Thus the Babylonians gave us the seven day week. Consider: SATURNday, SUNday, MOONday, do the rest in Spanish to finish the pattern.

The Greeks named the five wandering stars after their gods: Ermis, Aphrodite, Aris, Zeus and Kronos. They called them planetes, meaning wanderers. The Romans named them after their gods: Mercury, Venus, Mars, Jupiter and Saturn. More recently the last planet discovered received the name of the Roman god Neptune. If you think you’re the only one wondering why the seventh planet from the Sun received a Greek god’s name, Uranus, see page 49 of the script. If you think Pluto is still a planet, well, that’s in the script too.

The planets continue to fascinate us, but while the Hubble Space Telescope and planetary probes give us spectacular photos, to our eyes they remain spots of light in the night sky. Their size, distance and speed, unique for each planet, remain hidden to the casual observer. A scale model of our solar system allows us to see how vast space is, as even the fastest planet crawls along its orbit. The emptiness between the planets becomes obvious, as does the enormous size of the Sun compared to our own Earth.

While solar system scale models are common, this one is unique in many ways:

  • The State House dome provides a very visible center, high above Main Street, on a sunny day the newly applied gold leaf shining like our very own star.

  • There are multiple sites for the planets from which the dome can be viewed, as the entire orbit of the planet is defined. Other models just have one site for each planet, all of them lined up(which never actually happens).

  • Having multiple viewpoints along the orbits allows us to introduce something new to solar system models: Speed, how fast (or slow as you will see) the planet moves along its orbit.

  • Finally, if you don’t want to explore the planets in Concord, you can read a play about them.

IT ALL STARTS WITH THE SUN

Regardless of to what scale we choose to build our model, it will be impossible to see the whole thing from one spot. Just as Neptune is invisible to us without a telescope, we have no chance of seeing a model of Neptune from a model Earth if size and distance are kept to scale.

While the Sun would be visible from Neptune, without its great brightness it would be at the limit of naked eye perception. A small scale model which has Neptune relatively close to the Sun creates inner planets which are so small that a microscope would be needed to see them. Of course large inner planets results in Neptune being too far away to see. While you can pick any scale you want and build your own solar system model, the State House dome provides a perfect Sun. So if we know how big the dome is, we can compare it to the known size of the Sun and the ratio of those two diameters will determine the scale of our model. Thus the size of the dome determines the location, size and speed of all the planets. We just need to find out how big it is. That turned out to be more difficult than you might imagine…

THE STATE HOUSE DOME

First, a bit of background about the State House and the dome:

  • 1816- Construction began and was finished in 1819. The dome and eagle were present.

  • 1864- The building and dome were enlarged

  • 1940- Two thousand square feet of gold leaf was applied to the dome.

  • 1957- A new eagle, 6’6” high and 4’10” wide was put on, 150 feet above Main Street.

  • 1993 and 2016- New gold leaf was applied to the dome.

A visit to the New Hampshire Historical Society provides the above information and much more - except for the size of the dome. There is no chance you can ever get up there to measure it and a letter to the company that put on the gold leaf in 2016 went unanswered. And though we call it a dome, it is actually an octagon, not a hemisphere. Thus the distance across it varies by up to 8% depending on where you measure it. There are ways however to get an approximation of its size. Four different methods were used to determine how far across the dome is and they all yielded a similar result. All these methods have significant potential error but importantly the errors come from different sources, giving more confidence to the final answer.

  • A photo of the dome allows a comparison between it and the known width of the eagle. A simple ratio gives the width of the dome.

  • Knowing that 2000 square feet of gold leaf was used for the dome allows a calculation of the diameter of the hemisphere that would be covered by that. Since the dome is far from a perfect hemisphere and has a number of protruding features an assumption of 90% of 2000 was used.

  • Knowing the height of the dome over Main St. allows the creation of similar triangles and a determination of the diameter of the dome. This can be done by moving a known distance from the dome and holding up a small disc of known size and moving it from your eye until it exactly covers the dome.

  • Google Earth allows you to actually measure the dome.

    If you check the latitude from one side of the dome to the other along a given line of longitude you can figure out the distance. You just have to know how long a second of latitude is - actually a simple calculation since the ninety degrees of latitude from equator to pole is exactly ten million meters (not a coincidence, that’s how they decided how long a meter would be).

All four methods give about the same result: 32 feet or 10 meters.

To be sure I asked a third grader who was watching me stare at the dome. Being born in the 21st century, I was confident she knew the metric system so I asked her how many meters across she thought the dome was. She looked up at the dome, studied it for a while, then looked at me, made a face, shrugged her shoulders and threw up both hands, fingers outstretched in the air.

Yes. Confirmed. Ten meters!

Since the Sun is 1,392 million meters across, the ratio of dome to Sun is about: 1 to 140 million. Again, getting the exact dimension isn’t important as long as it’s in the ballpark of being correct. What is critical is to apply that same scale to every size, distance and speed in our model.

WHAT ELSE HAPPENS WHEN YOU MAKE SOMETHING 140 MILLION TIMES SMALLER?

  • The 7.8 billion people in the world number 55

  • One hundred years becomes 22 seconds

  • The speed of light is 5 mph

  • The water in an Olympic swimming pool is a tablespoon

  • A billion dollars is $7.14

  • Mt. Everest is as high as a human hair is thick

  • The Earth is a little more than three and a half inches across

  • The closest star is still far away- 180,000 miles.

THE PLANET ORBITS

The maps show the orbits of the planets as circles around the Sun. In reality, planet orbits are ellipses which are kind of like squashed circles. Some planets, like Mars and especially Mercury have very elliptical orbits while others like Venus and Earth are closer to being a circle. As a result, the distance from a planet to the Sun is always changing.

Earth is actually closest to the Sun in January. Since the Earth averages 93 million miles from the Sun, dividing by the 140 million scale gives about two thirds of a mile, or one kilometer for the radius of the Earth orbit in the model.

The maps show the average distance for each planet so the planet could be closer or further than the circles depict. Each site marked on the map is a location where the dome is visible. Dome views are limited beyond Mercury and Venus so a good view is not passed up just because it is between orbits. Can you find an outer planet view of the dome which is not on the map? Having the Sun behind you or to the side will make the dome more visible from the outer planets. Realize that the size of the dome from each orbit is what the Sun would appear like from that planet. Thus the dome views from the Earth sites will appear to be the same size as our Sun appears to us. Maps with GPS data are available at the Chamber of Commerce on 49 S Main St.

DO NOT LOOK DIRECTLY AT THE SUN, EVEN FOR A SECOND. PERMANENT EYE DAMAGE CAN RESULT. The Moon is a convenient substitute for the sun. Coincidentally, they appear identical in size to us.

Look for the 4 by 6 inch information signs at many view sites to learn the planet’s size and speed. The sign for the Sun is at Orange Leaf Frozen Yogurt at 70 N. Main St. The top of the dome can be seen across the street. What if you went over to Orange Leaf with three of your friends to have some froyo? What if you all left the store and looked for the planets? What might happen? What might you learn? Take a walk. Wander. And if you don’t want to walk the twenty miles to Neptune’s orbit, you can read the script and find out what happens...