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This is the moon and sky as seen through a telescope by an observer in Boston. And here the moon in the sky as if you were in Santiago Chile would see it. Put these two views together and you have an overlapping double image. What can we find out from this image. Could it possibly be a key to finding the scale of our solar system. It is.
A stunt I must say that the sun and the night. Different distances from us. Yet here we are bound to this incapable of icing over it for more than a few. Isn't it one of the most incredible things in science. That's Thomas should have been able to find out how far away this little back was. I want to describe how astronomers have made one of their most important measurements. The distance from the earth to the sun. When astronomers talk about this distance they dignify it by using the imposing term the patter lacks. What is pattern X when you can observe it fairly easily. Going up one finger and look at something
on the other side of the room. First close one eye then the other you can see how your finger seems to shift from side to side against the background. That pattern match shift is the pattern next on your finger and in fact pattern X is the Greek word for shift alteration. The parallax of your finger then is the angle made at your finger by the two lines of sight one from your left eye and the other from your right eye. Now bring your finger to your face and repeat the I played. Notice that the sheriff is great. You could use the shift pattern next to estimate the finger is from your face. The nearer right is the lodge in the pattern X would be. With this in mind if you look at the sky. If you want to detect the pattern X of an object in the Heavens it is easier to look at one that is nearby. Let's choose the nearest
the moon. Since it is near its Now next will be relatively large and it will be easy to see and measure. Here is a model of the moon. This time you can dance to make distance by closing your eyes alternately. Our eyes are only a couple of inches apart much too close together to give any shift effect of the moon. Instead it's place to observe us as far apart as possible on opposite sides of the earth. Nearly a thousand miles apart. Here is what each observer will see. You see our observers get frankly different views from their different spots. Now look at the background of stars and the foggiest and you can see the moons shift positions against that background. Now if you can measure the size of this chip you will be able to find the moon's distance.
The first problem here is how to fix positions in the sky so you can determine the angles of the ship. Well astronomers do it in just the same way the create fixed positions on the. How to Write for instance a spot on the air. We save the thinking is that latitude 20 degrees north and longitude one hundred fifty five degrees west latitude as measured from the equator and longitude from an arbitrary fixed circle that runs through the poles. Here's a cross-section of the longitude Mokhtar rounded covering 360 degrees to the circle you can see that they are expressed as angle. Latitudes are measured the same way. Astronomers look at the starry sky as if it were a vast globe inspecting the.
They draw an equator in the sky and also an arbitrary circle that goes through imagine riskiness they measure positions on this star map from these two lines just as we do on Earth from longitude and latitude. Therefore the positions of stars and distances between stars measured at angles in the sky. Now you can see how the moon's pattern X is measured. Here we have a distance between two observers. That is the diameter of the earth. Here is the moon and here the distance between the two positions of the moon is you're so right against the stars measured as an angle. So now you can draw a triangle and find this distance from the earth's center through the moon's center. We know the length of the base of the
triangle the diameter seven to nine hundred miles. Since we know the base angles of the triangle we can draw the whole triangle and by simple trigonometry you can calculate the height of the triangle. The distance to the moon which turns out to be about two hundred and forty thousand miles. It is clear that once you can determine the parallax angle of an object in the sky you have really solved the problem of how far away it is. The moon is a fairly easy subject when we try to measure the distance to the sun. The problem is a great deal more difficult. I'll show you why. Here you see the disk of the sun. And now you can see the shift of the digits as seen from opposite sides of the earth. Notice how small it is. Even if you could see the star
background which you caught the sound of pattern X would be almost impossible to measure. So you have to use a roundabout method. Suppose I show you a map of a section of the main curves with a scale missing. Imagine you are here and want to know how far it is to this island. What could you do. The island is in accessible. You cannot go there and measure the distance but you can go here and measure this distance. All right. Suppose that distance is 10 miles then you can measure how many inches it covers on the map and you find that it is 2 inches. Then you only need to measure the inches on the map to the island say 8 inches multiplied and you find that the island is 40 miles away. Can you play a similar trick in finding the distance to the sun. Could you make a
map in the correct proportions. Even if you didn't know the scale of this map possibly you could find a distance that can be determined and so determine the scale. Well this is exactly what astronomers do. Here is a model only of the so that if we had included the whole system intuitively in much too big to handle the sun is here in the middle and the planets are going around the sun in orbit. Here is the earth in its orbit and here is modest in its orbit outside the now. I'm going to move the planets so that they have both been aligned with the sun. Now let's move the earth around until they are in line with the sun again.
Astronomers call the interval between the times when the sun and earth and planets meet again in a straight line in the sand noted period of the planet found that it comes from a Greek word which means a meeting place. Now since the earth as it were going round its orbit almost twice before it meets Mars again in other words it would take almost two years before the Earth would be in a straight line with us and the sun again. It is easy to measure this side now to carry it off mobs seven hundred and eighty eight days. But the sign on a piano it doesn't tell us how long the plan it takes to go around the sun. It don't it tells us how long it takes for the planet and sun to be again to match the orbit of mas you must observe mas from two different positions when it is at the same point in its orbit and windy days at that same point.
The sun mas and some distant star will be in the map and you can see the earth and mas the epis gone twice now won't be in the same relative positions on the two separate occasions. Here they are with that this fine lined up with stars over there. Now if you carry miles around back to the same place the earth would have gone around nearly twice and will have arrived here. So we shall see Mas against a different background the star the problem is to find when we will be at a given point in its orbit. The odd thing is that it reaches a given fine regular nay every time it makes one trip around the sun. This interval is called the side you know to appear to the planet. How do you find this period. Well let's look at it
this way the earth is Siberia PSTN is 365 days so that it goes one three hundred sixty fifth all the way around its all that in one day. Now let's call the side the audio period of my X days since this is the unknown in our equation. Mars will go over X of the orbit in one day. Now you know that the earth goes around faster than Moscow so it catches up with us by 1 over 365 minus one over X of the second in a day which we know the whole time not a period. In other words the time taken by the ethic catch up with the game. It is seven hundred and eighty days. So in one day the earth catches up to modify one seven hundred eighty of the second. Now here is your equation. Three
hundred and six. It is equal to seven hundred and eighty eight. And the answer is it equals six hundred and eighty seven. So now you know the side getting a period of the time it takes to go around the six hundred eighty seven days. Now you and I need to pick today six hundred and eighty seven days a pop and you can observe Mars and knew it to be at the same point in its orbit but now look at the model again. On the first day three choose mas and the air and make a little mock to show where the yeah. Six hundred eighty seven days later Miles has gone around once and the air has
gone around not quite twice and is here now you have two different angles. You can measure it by viewing mas against the stock from the air to position. And you can draw this triangle with Maz at the apex. We also know the angle between the two positions of the earth. We know the time the kidlet between this faith and this one. We said that you know because the earth has gone round more than once and divide a year by the interval with these layers and get this angle so we know this angle we know these two angles and we can draw all this quadrilateral. We cannot place
exactly. This is our first hit. We have determined one point in the solar system but we haven't determined the scale yet. We only know the shape of their squad or natural and not its size. We could go on and plot the whole orbit of Mars in this way by measuring directions to Mars had pans of dates that was separated by six hundred and eighty seven days and you get the number of the quadrilateral like this one. In fact this is how Kepler first did it. You can also mak the orbits of the other planets and produce a map of the whole solar system. But what is the scale of this math you still don't know the distances. You still want to find the distance from the End up to the south. Remember the problem of determining the distance of the island from a map of unknown scales. Then you found a distance you could measure and you found the scale of the math by measuring that
distance on the map. You can do exactly the same thing with the math of the solar system. What you need to find is something in the solar system that has a rather large pattern. This means as you remember something nearby Mars and Venus the nearest planet. But even the pattern X-mas is quite small equal to its apparent that in Avatar when Mars is nearest to us Mars also is difficult to measure because it is not equally in human naked by the fact it shows sight faces in either way. In spite of these disadvantages Mars was the first than it used to measure the scale of the solar system. Mass was observed from two widely separated places on the earth. The angle of shift against the stock was measured and the distance was calculated in the same way as we determine the
moon's distance with this newfound distance the distance between the Earth and you can fix this scale of the mignonette in fact you can determine the whole scale of the solar system and we find that the distance from the earth to the sun is about 93 million miles. But astronomers kept looking for clues to objects that modify which they could measure this important distance. In 1897 they found a small planet with feigned name at the orbital era is ended lips at intervals of six hundred eighty three days. It comes inside the orbit of my eyes as you see in the model. When the earth is at the right its all of it. And is quite close to us and its parallax is nearly three times that of my eyes. This happened in 1951 the pattern
next to us so it could be measured accurately by using the diameter of the earth as we did for the moon. And since an arse is so small its position was not difficult to fix against the background of star the foundations of measurement taken of Andros give us a new determination of the distance within the planetary system the distance of the earth of the sun from the ethics of the sun. 93 million miles is not known within about 5000 miles. Assuming the plan actually is of any importance of the needs of the astronomers It is the basic unit to which all of a distance is in the universe referred. Naturally astronomers would have more than one method of measuring such a difficult and such an important quantity. Actually there are two or three other ways. Here is just one of them. Imagine if you could run a train running around on a circular track.
Now you want to find a distance across it. If this were the diameter of the track would be a trifle distance from the end to the sun where you can find out the distance around the track the circumference immediately. If you know how fast the train is going about long it takes to get around the pressure. Suppose the train is going at 60 miles an hour and it takes 10 hours to go. Then you know that six hundred miles around. And from this point you can use the well known formula the ratio of the circumference to the diameter of a circle is equal to the constant. Try 3 4 1 4 1 5 9. So if you could find the diameter by dividing this conference by pi you would know the size of the track. Now you know how long it takes the Earth to go round its track. It takes a year. If you could measure the speed at the end then you could calculate the circumference and
the diameter of it all that at once. But can you measure its speed. Astronomers do it by using a property of light which is called the Doppler effect. If you haven't noticed the sound of a train whistle as it passes you the picture of the sound drops abruptly you hear this because the waves of sound crowded up towards you as the train approaches and does it receive the more crowded the waves the higher the pitch of the sound will be. If you had a good enough or some way to measure the pitch you could even measure the speed of the train by measuring the change in pitch. Now we happen to have a recall of the sound of a jet plane as it comes from far away on the Fosses at some distance in front of us and goes away to our right. This sound effect is not as simple as that of the train because the speed with which a jet plane first approaches
us and finally recedes it is changing continuously. The sound you hear is very high pitched up goes down gradually and settles down with a low a pitch. Listen. Let's hear it again. Now how does this relate to the style of course we can't listen to the stuff. But they do say not to light this light comes in waves. We too are affected in the same way. If the light source.
When the lights are off approaches you the light grows somewhat when it goes away the light becomes red. Astronomers can measure accurately this blueing and reddening of light and determine the speed of the Source of All Star the greater the change in color the greater the speed. Suppose you were on a. You receive from the what. The measure the change in color and pride to be at this point. Seems to be approaching the feet of this. It could be receiving the ripples. So it is possible to measure the speed of the earth in its orbit and then you can find the circumference of the circle and you can multiply the number by the number of seconds in a year and that gives you the circumference of the Earth's orbit. Then of course you use to try to get the diameter of.
It. And there you have another way of determining the set of parallax. But wait a moment. You cannot conduct an observation from a star. However you can observe that the earth and as the Earth moves around in its little bit you will see this appear to approach you and to move away from you when you are here. Actually of course the stock is stationary. Therefore the speed you measured by watching the night shift of a star is actually the speed of the earth in its orbit. So you have again solve the puzzle of the distance to the sun. Babs having the light ship far away you have seen several ways in which astronomers have measured the scale of the solar system. We measure the distance of the moon and the distance to SRS from opposite sides of the earth. Here are in other words you used for the earth's diameter seven to nine hundred
miles as a baseline. In this way you determine the scale of the solar system and measure the distance of the sun. Now you want to go out beyond the solar system to the stocks with only our humble yardstick of seven thousand nine hundred miles. We could not possibly observe the pattern acts of anything outside the solar system. Indeed we cannot even measure directly the distances of most things inside the solar system. But the jump from 7 to 900 to 93 million miles extends our reach enormously as far as the nearest star from opposite sides of the Earth's orbit. You can see a small pattern electic shift for several thousand stars. It is very small even for the nearest star. It is less than a minute of OC. And remember there are 360 degrees to a circle and 60 Minutes to a degree so that twenty one thousand six hundred minutes of our two a circle
and you have to be very accurate indeed to measure an angle as small as one twenty one 600 a circle. But still it has been done for several thousand stars and we can tell their distances and their true absolute brightness. You can measure the distance to one star and then pick out another similar star. Assuming its brightness is the same you can deduce its distance even though the stars so far away that it's pattern X couldn't possibly be measured in this way. Astronomers have stepped from one measuring stick to another and are now measuring distances out to the fastest observable object in the universe. Well here we are then the impossible has happened.
And I asked one of us have found out without leaving the Earth that the sun is 93 million miles away. Why did this seem so impossible in the first place. I would say that that was because when you and I look at the stars we do so for one minute at that time but means we don't really know with them. But if you keep observing them night after night as astronomers have done from the earliest this times to ours then you become familiar with them and you begin telling them of how you relate to it much later. You find that your night days even even the wanding of Mars and this Mrs. Gamp are sick and told us how the public began to be and I have stated without to technical devices the telescope and the photographic plate astronomers could never have obtained such decision as measuring 93 million miles within an hour
of five thousand. Such an exact Was it tiresome of us tunnel most of our own generation invest one of me at any rate we find no guile for being ashamed of our age.
Of Science and Scientists
Episode Number
The Distance to the Sun
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Episode Description
Hold up one finger at arm's length and look across it to an object on the far side of the room. Looking at the object, first close one eye and then the other. You'll see that your finger seems to shift from side to side against the background. This shift, Cecilia Payne-Gaposchkin (Professor of Astronomy and Phillips Astronomer, Harvard University) shows, is the parallax of your finger, and parallax is the key to finding the scale of the universe in which we live. Using parallax, a number of astronomical models, and even a toy train, Mrs. Gaposchkin shows how astronomers find the distance to the sun, one of the basic steps in establishing a scale for our solar system. She indicates that though the method is relatively simple, the value for this distance is staggering: 93,000,000 miles. And yet, as astronomy reaches farther into the universe of galaxies, this becomes a relatively short distance. Confronted with such enormous figures, the non-scientist reacts at first with disbelief. The methods used to produce them, explained in this episode, will help to make astronomical measurements credible. (Description adapted from documents in the NET Microfiche)
Series Description
Americans tend to think of the sciences as potentially useful (air-conditioning) or potentially troublesome (Strontium-90). We accept or marvel at the revolutionary products of science while giving little thought to the basic ideas, concepts, techniques and logic that have gone into exploring, understanding and explaining our universe or in building our technical civilization. Such an understanding of science does not come easily. Limited by time and opportunity, scientists do not often explain themselves to non-scientists. Also, the quality of science is most difficult to the layman to understand is its indirect approach to the discovery of truths. Robert Frost summed up the problem by commenting that to his mind all science rested on the question, "How she differs from what she's like."Without attempting to teach physics or chemistry or geology, these programs suggest the qualities and outlook of science. By analogy and demonstration, they reveal the ideas which guide scientific research and the truths that research uncovers. They give an appreciation of what the scientist can and cannot do. As one speaker says, "The important thing about science is not merely that it gives rise to technological miracles, but that it provides us with one of many guidebooks we need to find our way in this universe." Today, as non-scientists are called upon to make decisions or concur in decisions that may affect the future of scientific research and even the future of life, a knowledge of "how she differs from what she's like," may not only be useful, but necessary. By explaining and demonstrating the guiding principles of science and scientists, these programs attempt to convey that increasingly necessary knowledge. Produced by WGBH-TV, Boston, the producer-director was David Walker and the executive producer Lawrence Kreshkoff.Dr. Phillipe Le Corbeiller is Professor of Applied Physics and of General Education at Harvard University. He is host and program editor for Harvard in the television series, "Of Science and Scientists." A leader in Harvard's general education program since its beginning in 1946, when he started the course, "Principles of Physical Science," Dr. Le Corbeiller was the first to be appointed professor of General Education in 1949, in addition to being professor of Applied Physics. Throughout the series Dr. Le Corbeiller is joined by other scientists. (Description adapted from documents in the NET Microfiche)
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Camera Operator: Walcott, Charles
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Chicago: “Of Science and Scientists; 8; The Distance to the Sun,” 1957-00-00, WGBH, Library of Congress, American Archive of Public Broadcasting (GBH and the Library of Congress), Boston, MA and Washington, DC, accessed January 30, 2023,
MLA: “Of Science and Scientists; 8; The Distance to the Sun.” 1957-00-00. WGBH, Library of Congress, American Archive of Public Broadcasting (GBH and the Library of Congress), Boston, MA and Washington, DC. Web. January 30, 2023. <>.
APA: Of Science and Scientists; 8; The Distance to the Sun. Boston, MA: WGBH, Library of Congress, American Archive of Public Broadcasting (GBH and the Library of Congress), Boston, MA and Washington, DC. Retrieved from