It is a great deal easier to talk about things outside our reach, such as the Sun and Moon, by imaginary scale models. Real scale models require very large paper. The earth and moon can be diagrammed on a page this size as a 1/2 cm circle for Earth and a 1.5 mm circle for the moon - separated by about 16 cm. At this scale, the sun would be about 65 meters (71 yds) away and about 55 cm in diameter. Space is BIG. Just for Sun, Earth, and Moon, we need a football field! [ Or a magnifing glass to see the moon.] Pluto is 39.6 times as far away from the sun as the earth. At our scale, that's about 1.6 miles. We can get Earth and Moon on our paper, but need a jet sized airport to model the solar system. [So we talk about it, but we seldom actually make a model exactly to scale.]

Another problem turns up - time! It is different everywhere. [I assume you want to look at the various bodies.] We see the Moon about 3 seconds away, the sun is 8 minutes, Pluto is about 5.3 hours. The nearest star is 6 years. You can not see what is going on in the solar system at any particular exact time! [Well that's not exactly true. If you are a light year away, and equidistant from say Earth and Sun, what you see is "exactly" a year ago. Suppose you have a friend on Earth and one on the Sun. You would observe their watches reading exactly midnight (a year ago). But each of them would see the other's watch 8 minutes slow!]

Ellipses Yes, the earth's orbit is indeed an ellipse, but it is very close to circular. The Sun is at one foci. Earth will be closest to the sun on 2 Jan 2000 (91,405,436 miles) and farthest away on July 3 (94,511,989 miles). These dates vary each year by a day or so. The difference in distance to the sun is 3,106,553 miles; (about 3.3% ). That's enough to make precise sundials hard to construct. The problem is not the distance, it is due to the speeding up and slowing down of an object in an elliptical orbit. (The path wipes over the same area per unit time.)

The orbits of the planets are very close to circular. If you draw Earth's orbit on this piece of paper, and then draw a circle of the same size, you will need a fine pencil. The difference will be close to thickness of a normal line.

In the space below, draw a scale model of the earth and moon. Put Earth at the left - a 5 mm circle. Then a horizontal line 16 cm long to a 1.5 mm circle for the Moon. The sun will take more than two pages and they must be 71 yards away at this scale.

Seasons
Light rays hitting a surface at an angle spread out over a larger area and are therefore at a reduced intensity. The axis of rotation of the earth is tilted about 23 degrees from the plane of the orbit, and is not affected by the earth's revolving around the Sun. If there were no tilt, the sun would be directly over the equator (somewhere) all day and every day. If you lived on the equator, the sun would rise at the same place in the East in the morning and set at the same place in the West every night. The equator would get the "direct" sunlight and would be hot! As you go away from the equater the rays come in at an angle and are less intense. It would therefore be cooler. At the poles, the sun would be seem to be rotating around the horizon and you would be cold all the time. I can not go further with this, but aside from being boring, there could be other "side effects". What would the weather be like? How would vegetation be affected? etc.

However, we do have a tilt. Due to this tilt, the angle of incidence of sunlight varies over a year's time, especially in the temperate zones. [At Boston, the angle to the sun at noon is 24.4 degrees in December and 71.5 in June.] It is this variation that causes winter to be cold, and summer hot. [It is not the distance! Recall that we are closer in January.] In the tropics, the sun's elevation at noon is much higher, and it varies less. In the tropics, there is always one latitude where the Sun will be directly overhead at noon. At the poles, the sun disappears below the horizon for 6 months! In the summer, the sun appears to travel in a complete circle around us - always a little above the horizon! [It dips a bit, but does not set until winter.] I wonder how long it takes for the sun to set at the North Pole. That is, from the time it dips to just touching the horizon to the time it just disappears, and does not come up until Spring. (I asked an astronomer friend and he thinks it would take 24 hours - but he has not been there. If you know anyone who HAS, ask him and let me know!)

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Problems:

1. What would the movements of the moon look like from a point way out in space on a line perpendicular to the plane of the Earth's orbit starting at the Sun and about as far from the Sun as Pluto?

2. Would the Moon have phases from this point?

3. What would it look like, and how would it move, if viewed from the North Pole? Note: The new planetarium in New York City can show you these views!

Here are a few unpolished thoughts I have had on Astronomy.

The human race has always wondered about where we are, how we got here, and where we are going.
For example:
Q. What holds the "World" up?
A. Atlas, the giant.

Q. What is he standing on?
A. The back of a giant turtle.

Q. And the turtle?
A. On the back of another turtle - and other turtles down ad infinitum into the unfathomable abyss.

Q. What about the Sun and the Stars?
A. The Stars are fixed on the celestial spheres and rotate around the earth day and night. The sun is pulled across the sky in a celestial chariot.

Q. What about the "wanderers" i.e. the Planets?
A. Each has its own celestial sphere, and a complex path it must follow. All the spheres are transparent. [The moon has one too.] Or, for a more modern version, you could say:

Q. What holds up the Earth?
A. Nothing! The Earth is falling.

Q. It's falling down?
A. Not really "down". It is just following the "force".

Q. What force?
A. The force of Gravity.

Q. Where does that come from?
A. It seems to come from every mass that exists. For every pair of masses, the force of gravity between them is directly proportional to the product of their masses, and inversely proportional to the square of their separation. For the earth, the biggest force comes from the gravitational attraction of the Sun. For you and me it is the Earth's attraction to our mass that matters. [We call it our "weight".] You must be touching the bigger mass to feel the force. When you are falling, you still have your mass, but you can't feel the force, so you're "weightless". Your "weight" is the force. Your "mass" is the amount of stuff you are made of. Your "weight" is proportional to your mass - the more stuff, the greater the force or weight. It is also proportional to the other mass. You "weigh" more on Jupiter, and less on the Moon.

Q. Where are we going?
A. Well first, we are going around the Sun, and of course it is falling through space too.

Q. What is "space"? A. Nothing at all. It's like the unfathomable abyss.

Q. Where are the stars?
A. In space too, and falling just like us.

Q. If they are falling, how come they move all together. How come the night sky looks so much the same from night to night?
A. It does not look exactly the same, except for one star - Polaris - the North Star. [Assuming you live in the Northern Hemisphere as I do.] All the other stars seem to rotate counter clockwise around Polaris. We see them rise in the East and set in the West - just like the Sun does. An easy way to describe what we see is to assume the world is a ball that is spinning - once around in 24 hours. We see the sun half the time, and the stars the other half. The sun and stars seem to be moving around us, but it is easier to describe it all if the earth spins.

Q. OK, but why does the scene change from month to month?
A. It's because the spinning earth is falling around the sun, at an average distance of about 93 million miles. The stars are so far away that even 93,000,000 miles is very small. Have you noticed that when you drive along the highway, the houses and trees on the horizon move a lot slower than the telephone poles by the side of the road? It's like that! We are doing the moving!

Q. Why does it take a year?
A. Because that is how we define the word "year" ! We just observed the sky and found out that it changes, but then it repeats itself. If you look at the Big Dipper every week at the same time you will see that it is slowly moving around the North Star! The length of time it takes to go all the way is called a "year". What is a "Day"? How about a "month"? A "day" is the average time from one sunrise to the next one. A "month" was once based on the average time it takes for the moon to go through its changes. (About 28 days. No doubt you have heard Native Americans start a story with "Many, many moons ago, ...) Our calendar has had political influences. July and August were added to honor Julius and Augustus Caesar. Our "months" are not the same length. The date of Easter is still set by reference to the Moon.

Q. If the stars, planets, moons, asteroids, meteorites, and Cosmic dust particles all are falling, why don't they bump into each other?
A. The small ones do bump into the large ones. Thousands of small meteorites hit the Earth daily. If you consider the stars, there seems to be another thing going on. Its like the spots on a polkadot balloon. When it is being blown up all the spots move farther apart. Observations show that on a grand scale, this is happening in space too. The separation between stars is increasing! On a local scale, the Earth is going around the Sun, and the Moon around the Earth. It has been discovered that once you have a velocity, it takes a force to change it or to change its direction. The force of gravity between us and the Sun is constantly changing our direction - keeping the Earth in orbit - but it is not strong enough to pull us in! This arrangement has been stable for millions of years, and is likely to be going this way for millions more. [If you prefer to talk in billions of years, you may "see" some changes...]

Q. If the stars are all falling, how does your model show that the constellations should stay the same?
A. We conclude that they are far far away! The nearest star is about 4 lightyears away. Its direction changes by about 1.6 seconds of arc from one side of our orbit to the other. [There are 3600 seconds of arc to the degree.] There are fewer than 100 stars that are close enough to show a measurable change in direction in six months. (The time it takes us to get to the other side of our orbit.) If you point your telescope at the same constellation and take a picture every week for a year, some of the stars will line up perfectly. They are the ones that are truly far away. The "closer" ones trace out small ellipses when you superimpose all the pictures. Note also that the grouping we call "constellations" is just how it looks to us. The stars that look like a big dipper to us would look far different from some other place in space. It is unlikely that they would even seem to be together. [The "celestial spheres" had them all on the same sphere. We have them as independent bodies, and at different distances from us.] Question: Is our version really easier to accept than Atlas and the turtles? At least they had an unfathomable abyss in only one direction. Ours goes abysmal in ALL directions! Theirs had a center. Ours does not seem to.

An imaginary trip...

Suppose you took off in a spaceship in August heading for Capricorn, i.e. directly away from the sun. [We all know the Sun is in "Leo" in August, and that Capricorn is opposite Leo, on the other side of the sun.] Once you were beyond Pluto's orbit, you could look back at the sun without going blind. The sun would be a real bright star in Leo. As you move along, Leo would look about the same, but the stars around it would change a little. Earth and the other planets would be too dim to see. And if you were to look forward, the changes in Capricorn would be more obvious. When we get close enough for the nearest star to be bright enough to hurt our eyes, Capricorn would look very different indeed. Our "Old Sol" would still be in Leo and much dimmer. Leo would look smaller perhaps, but still recognizable. The rest of the sky would be distorted. But won't we think that WE are at the center of the Universe? After all we will see stars in every direction! OK...How do we get back home?

All we need to do is turn around and head back to "Sol". We know old Sol is that new star in Leo, and Leo is a little smaller, but not very distorted. Where will Earth be? Well, of course, it has been going around old Sol all this time at a fairly constant distance of 93 million miles. We should be able to spot it fairly quickly.

It has been easy to make this trip in our imagination. As we see things, it is a long way to Capricorn. At the fastest speed we can now achieve, it would take many lifetimes to do it. But it was fun to imagine it! [How long does it take to go a lightyear away and return to Earth at 25,000 miles per hour? Note: light travels at 186,000 miles per second. My calculations show it takes about 53,568 years to go 1 lightyear away and return! And the nearest star in Capricorn is many lightyears away! ]

We have learned from complex experiments that there is a natural limit to speed. You can't go faster than the speed of light! Theory shows that even "time" is not as simple as it looks. For example, would you believe that the astronauts that went to the moon are a few seconds younger than they would be if they had stayed home? It is a more complex universe than it seems to be! It also becomes difficult to draw the line between "real" and "theoretical". BUT for us, it is easy. We just postpone the things that are too much. In college, we will have the mathematical tools (Things like Algebra, Trigonometry, Calculus...) to make sense of more complex models and theories, and new instruments (tools like the Hubble telescope) to uncover more complex things.