Astronomy

Precision in the measurement of the distance to the Sun

Precision in the measurement of the distance to the Sun


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How precisely can the distance to the Sun be measured? Wikipedia says the distance to the Moon can be measured upto millimeter precision. But Wikipedia article on distance to the Sun says only about Astronomical Unit and nothing on the precision of the measurement of the distance to the Sun. I am certainly aware that we now use radar to measure the distance to the Sun, and I remember reading the precision in its measurement somewhere on the Internet, but I can't find it anymore. When I try to find the relevant information on the Internet, all I find is educational articles on things such as parallax, which is certainly superceded by radar measurements, or articles on lunar distance, which I am not looking for. Relevant references will highly be appreciated.

Edit: I just found out on Internet that we measure the distance to the Sun through distance to the Venus or Mercury. Anyway I want to know the precisions or errors in these measurements…


This is a partial answer too long for a comment, but it may help to get the ball rolling…

Starting from this answer we can see that the standard gravitational parameter of the Sun used by JLP in their development ephemerides is1.32712440040944E+20. While that doesn't mean we know the Earth's orbit to 1 part in $10^{14}$ it hints that it's believed to be known surprisingly well!

It's possible that something like this might shed some light on the subject, but it's not an easy question to answer. The Planetary and Lunar Ephemeris DE 430 and 431, IPN Progress Report 42-196 (February 2014) Part of the problem is that we don't know exactly where the solar system barycenter is with respect to the Sun because there may be bodies far away we haven't detected yet. That's only a small effect on the Sun-Earth orbit. If I had to guess, I'd say it's somewhere between 1 and 100 meters uncertainty between the Earth and the center of the Sun. Where the edge of the Sun falls is a horse of a different color!


Uncertainty in the distance between Sun and other planets

I have read about the orbit distances between Sun and the planets and have come to know for example: Earth is around 150 million km away from the Sun.

However I have seen that tht value is only an average radius of the orbit.

I however cannot find the uncertainty of this measurement.

I have considered the eccentricity of the planets and thought of using it to determine uncertainty.

So then I would have: Earth distance from Sun = $(150 imes10^6pm 2.5 imes 10^6)km$. As Earth's eccentricity is around 0.017

So I am wondering if this would be the right way to determine the uncertainty of the radius of the orbit distance.


The Metric System

One of the enduring legacies of the era of the French emperor Napoleon is the establishment of the metric system of units, officially adopted in France in 1799 and now used in most countries around the world. The fundamental metric unit of length is the meter, originally defined as one ten-millionth of the distance along Earth’s surface from the equator to the pole. French astronomers of the seventeenth and eighteenth centuries were pioneers in determining the dimensions of Earth, so it was logical to use their information as the foundation of the new system.

Practical problems exist with a definition expressed in terms of the size of Earth, since anyone wishing to determine the distance from one place to another can hardly be expected to go out and re-measure the planet. Therefore, an intermediate standard meter consisting of a bar of platinum-iridium metal was set up in Paris. In 1889, by international agreement, this bar was defined to be exactly one meter in length, and precise copies of the original meter bar were made to serve as standards for other nations.

Other units of length are derived from the meter. Thus, 1 kilometer (km) equals 1000 meters, 1 centimeter (cm) equals 1/100 meter, and so on. Even the old British and American units, such as the inch and the mile, are now defined in terms of the metric system.


There never has been a direct measurement of the distance between the Earth and the Sun. The best we can do is measure the distance between the Earth and the other planets, and from that infer the distance between the Earth and the Sun.

Today's estimates aren't based on radar pings from Venus. That is so last millennium! Early 1960s, to be precise. That said, estimates of the astronomical unit made possible by those 1960s radar measurements of the distance between the Earth and Venus were much more precise than were prior estimates based on parallax, reducing the uncertainty in the astronomical unit from 16000 km to less than 1000 km.

In the 50+ years since that time, space agencies have sent spacecraft to all of the other seven planets in the solar system (other than the Earth, of course), plus Pluto, plus some asteroids, plus some orbiting the Sun. The telemetry from those spacecraft, augmented by very long baseline interferometry (VLBI), have made those measurements from the 1960s look rather imprecise. The latest work was in 2009 by Pitjeva and Standish, who stated the uncertainty in the astronomical unit as being 3 meters. No work has been done on measuring the AU since then because the astronomical unit is now a defined quantity, exactly 149597870700 meters (the value stated by Pitjeva and Standish).


Measuring the Distance of the Sun from the Earth*

THE distance of the sun from the earth or, speaking more correctly—for the distance is, of course, variable—the semi-major axis of the earth's orbit, is the most important constant in astronomy. It determines the scale not merely of the solar system but also of the whole universe. It enters into almost any calculation of distances and masses, of sizes and densities, either of planets or of their satellites or of the stars. Any error in its determination is multiplied and repeated in many different ways. The measurement of the sun's distance with the highest attainable accuracy is therefore of great importance in astronomy, and it is not surprising that vast amounts of time and labour have been devoted to it by astronomers in the course of centuries.


After Hundreds of Years, Astronomers Finally Agree: This Is the Distance From the Earth to the Sun

How far away from Earth is the sun? Not just, you know, very, very far, but in terms of an actual, measurable distance? When you're calculating, how do you decide which location on Earth to measure from? How do you decide which spot on the path of Earth's orbit will serve as the focal point for the measurement? How do you account for the sheer size of the sun, for the lengthy reach of its fumes and flames?

The measurable, mean distance -- also known as the astronomical number -- has been a subject of debate among astronomers since the 17th century. The first precise measurement of the Earth/sun divide, Nature notes, was made by the astronomer and engineer Giovanni Cassini in 1672. Cassini, from Paris, compared his measurements of Mars against observations recorded by his colleague Jean Richer, working from French Guiana. Combining their calculations, the astronomers were able to determine a third measurement: the distance between the Earth and the sun. The pair estimated a stretch of 87 million miles -- which is actually pretty close to the value astronomers assume today.

But their measurement wasn't, actually, a number. It was a parallax measurement, a combination of constants used to transform angular measurements into distance. Until the second half of the twentieth century -- until innovations like spacecraft, radar, and lasers gave us the tools to catch up with our ambition -- that approach to measuring the cosmos was the best we had. Until quite recently, if you were to ask an astronomer, "What's the distance between Earth and the sun?" that astronomer would be compelled to reply: "Oh, it's the radius of an unperturbed circular orbit a massless body would revolve about the sun in 2*(pi)/k days (i.e., 365.2568983. days), where k is defined as the Gaussian constant exactly equal to 0.01720209895."

But rocket science just got a little more straightforward. With little fanfare, Nature reports, the International Astronomical Union has redefined the astronomical number, once and for all -- or, at least, once and for now. According to the Union's unanimous vote, here is Earth's official, scientific, and fixed distance from the sun: 149,597,870,700 meters. Approximately 93,000,000 miles.

For astronomers, the change from complexity to fixity will mean a new convenience when they're calculating distances (not to mention explaining those distances to students and non-rocket scientists). It will mean the ability to ditch ad hoc numbers in favor of more uniform calculations. It will mean a measurement that more properly accounts for the general theory of relativity. (A meter in this case is defined as "the distance traveled by light in a vacuum in 1/299,792,458 of a second" -- and since the speed of light is constant, the astronomical unit will no longer depend on an observer's location with the solar system.) The new unit will also more accurately account for the state of the sun, which is slowly losing mass as it radiates energy. (The Gaussian constant is based on solar mass.)

So why did it take so long for the astronomy community to agree on a standard measurement? For, among other things, the same reason this story mentions both meters and miles. Tradition can be its own powerful force, and the widespread use of the old unit -- which has been in place since 1976 -- means that a new one will require changes both minor and sweeping. Calculations are based on the old unit. Computer programs are based on the old unit. Straightforwardness is not without its inconveniences.

But it's also not without its benefits. The astronomical unit serves as a basis for many of the other measures astronomers make as they attempt to understand the universe. The moon, for example, is 0.0026 ± 0.0001 AU from Earth. Venus is 0.72 ± 0.01 AU from the sun. Mars is 1.52 ± 0.04 AU from our host star. Descriptions like that -- particularly for amateurs who want to understand our world as astronomers do -- just got a little more comprehensible. And thus a little more meaningful.


Precision in the measurement of the distance to the Sun - Astronomy

Measuring Radial Velocities
Radial velocity is measured in terms of the change in the distance from the sun to the star. If this is increasing (the star is moving away from us), the radial velocity is positive if it is decreasing (the star is moving toward us), the radial velocity is negative. We cannot use the radial velocity to decide whether the star is "really" moving toward or away from the Sun or vice-versa what it measures is the relative motion of the Sun and star. To measure some kind of absolute motion in space we would have to define a reference frame based (for example) on the average motion of stars in our vicinity. This would involve a tremendous amount of work, and as we learn more might prove to be no more useful.
The radial velocity of a star is measured by the Doppler Effect its motion produces in its spectrum, and unlike the tangential velocity or proper motion, which may take decades or millennia to measure, is more or less instantly determined by measuring the wavelengths of absorption lines in its spectrum. This can be accomplished regardless of the star's distance from the Sun, providing that it is bright enough to observe its spectrum in the first place. The only way that the star's distance affects the measurement is that the further away it is the fainter it appears, and the longer it takes to collect enough light to observe its spectrum. For the small radial velocities observed for stars in our own Galaxy the percentage change in the wavelengths emitted by the star, compared to their normal wavelengths, is the same as the star's radial velocity as a percentage of the speed of light. For instance, if the wavelengths are 1/10th of 1 percent less than normal, the star is moving toward us (or we are moving toward it) at 1/10th of 1 percent of the speed of light, or about 100 km/sec (which is actually a fairly high value) if the same percentage change were observed, but at a wavelength longer than normal, the star would be moving away from us at that speed.
Unlike proper motion, which can only be measured for nearby objects, radial velocities can be measured for any object, even the most distant galaxies ever observed. Because of the expansion of the Universe, distant galaxies may be receding from us at thousands or even tens of thousands of km/sec. In such cases the percentage change in the normal wavelength is not the same as the actual recessional velocity (a term used in place of radial velocity when the distance is so large that objects at that distance are always "receding" from us), and special relativistic calculations have to be used. As an example, in the NGC/IC/PGC catalogs on this site, if the recessional velocity exceeds 7000 km/sec (a little over 2% of the speed of light) I list a distance calculated from the percentage change in wavelength, then the more accurate distance calculated using relativistic corrections.

Topics to be added or linked to at a later date

Background Physics: The Doppler Effect
(Discussion of the Doppler Effect, and how it can be used to measure radial velocities merely hinted at above.)

Caveats
(Discussion of correcting for the Earth's orbital motion)
(Discussion of correcting for perturbations of our motion, e.g. due to the Moon)
(Discussion of correcting for the elliptical shape of our orbit, with a notable historical oversight)

Radial Velocities in Multiple Star Systems
(Discussion of variable radial velocities, and their causes: lead-in to Spectroscopic Binaries)
(discussion of using radial velocities to determine the masses of stars, clusters of stars, and galaxies)

Radial Velocities in the Universe
(Discussion of the radial velocities of galaxies: lead-in to The Expansion of the Universe)


The distance between Sun and Earth mentioned in Hanuman Chalisa

The shape of Earth’s orbit around the sun is not a circle and is slightly elliptical. Therefore, according to modern astronomy and science, the distance between the Earth and the Sun varies throughout the year.

source

The nearest point in the earth’s orbit is known as Periapsis (Perihelion) at which the Earth’s orbit around the Sun, the Earth is 147,166,462 km from the Sun. It usually occurs around January 3. The farthest point in the earth’s orbit is called Apoapsis (Aphelion) when the earth is farthest away from the sun around July 3 when it is 152,171,522 km. Hence, the average distance between the Earth and the Sun is 149,597,870.691 km.

Modern scientists measured the distance between the Sun and the Earth for the first time in 1672 which was by Jean Richer and Giovanni Domenico Cassini. They measured the distance between the sun and earth as 22,000 times of the Earth’s radius (Total Distance: 220000 x 6371 = 140,162,000 km).

source

However, the Hindu texts such as the Vedas and Upanishads have guided the Indian civilization for thousands of years. They are considered as the pillars of Hinduism. ‘Veda’ which basically denotes ‘Knowledge’, is a collection of observations and information that goes well beyond the comprehension of ordinary human beings. It consists of information that delves into various branches of science such as astronomy, physics, chemistry etc. One solid example is the calculation of the distance between the Sun and Earth mentioned in the Hanuman Chalisa.

The fact that the distance between the Sun and Earth was accurately measured 2 centuries before the modern scientist is probably one of the most astounding facts of Hinduism. The well renowned Hanuman Chalisa, authored by Goswami Tulasidas who was born in the 15th century. The Hanuman Chalisa is known to have accurately provided the distance between the Sun and our planet Earth. This fact basically means that this scientific information was discovered 2 centuries before the 17th-century scientists.

Based on scientific findings Earth is farthest away from the Sun around July 3rd when it is 94,555,000 miles (152,171,522 km) away. This point in the earth’s orbit is called Apoapsis (aphelion). The average distance from the earth to the sun is 92,955,807 miles (149,597,870.691 km).

The Hanuman Chalisa prayer mentions about the distance between the Sun and Earth:

‘“जुग सहस्र जोजन पर भानू। लील्यो ताहि मधुर फल जानू॥ १८ ॥”

– Juga Sahastra Yojana Para Bhanu, Leelyo Thaahi Madhur Phala Jaanu

Which means,

Sun is at the distance of sahastra (thousand) yojan (an astronomical unit of distance).

The Hindu Vedic literature states the values of the variables such as:

1 yuga = 12000 celestial years,
1 sahastra = 1000 &
1 yojana = 8 Miles

Yuga x Sahastra x Yojana = Para Bhanu
12,000 x 1000 x 8 miles = 96,000,000 miles
1 mile = 1.6kms
96,000,000 x 1.6kms = 153,600,000 kms to the Sun.

After certain intellectuals decoded this famous line of Hanuman Chalisa by Tulsidas they could find the distance of Earth, they found that it is exactly the same as that discovered by scientist later. However, the Earth will have slight variations of distance to the Sun based on the different season because it moves around the Sun in an elliptical manner.

It is very interesting how it is mentioned When Hanuman was very young, he flew from Earth to the sky in the direction of the Sun to eat it, assuming it to be a ripe, luscious fruit. Tulsidas while stating this incident in the Chalisa in simple languages gives the distance between the Earth and the Sun.


Earth-Sun Distance Measurement Redefined

One of the stalwart units of astronomy just got a makeover. The International Astronomical Union, the authority on astronomical constants, has voted unanimously to redefine the astronomical unit, the conventional unit of length based on the distance between the Earth and the sun.

"The new definition is much simpler than the old one," says Sergei Klioner of the Technical University of Dresden in Germany, one of a group of scientists who worked decades toward the change, which took effect last month during an IAU meeting

Under the new definition, the astronomical unit (or AU) the measurement used for the Earth-sun distance — is no longer always in flux, depending on the length of a day and other changing factors. It is now a fixed number: 149,597,870,700 meters, which is the equivalent of almost 92.956 million miles.

Klioner explained the simpler definition is helpful, for instance, for scientists who formulate ephemerides — tables that give the precise position of astronomical objects in the sky. They utilize the astronomical unit to calculate the motion of bodies in the solar system. [Solar System Explained From the Inside Out (Infographic)]

"The broader community of astronomers are able now to better, with less efforts, understand what their colleagues — astronomers who are experts in planetary ephemerides — do and how they produce the high-accuracy theories of motion in the solar system," he told SPACE.com by email.

The revision also makes the unit easier for engineers, software designers and students to understand, Klioner and his colleague Nicole Capitaine, of Paris Observatory, noted.

At the same time, the redefinition can serves an epitaph to the bygone era when Earth-bound scientists depended on viewing angles to calculate celestial distances.

An established unit

Lacking precise instrumentation, early astronomers relied heavily on angles to calculate the size of the universe. By studying Mars from two separate points on Earth, 17th-century Italian astronomer Giovanni Cassini was able to use trigonometry to calculate the distance from Earth to the sun with only about a 6 percent error.

"Expressing distances in the astronomical unit allowed astronomers to overcome the difficulty of measuring distances in some physical unit," Capitaine told SPACE.com by email. "Such a practice was useful for many years, because astronomers were not able to make distance measurements in the solar system as precisely as they could measure angles."

Modern instruments can come within a few meters of exactly determining distances of nearly150 billion meters (150 million kilometers), or some 93 million miles.

The astronomical unit eventually came to be defined by a mathematical expression that involved the mass of the sun, the length of a day, and a fixed number known as the Gaussian gravitational constant. Because the Earth orbits its star in an ellipse rather than a circle, the length of a day shifts over the course of a year. At the same time, the sun is constantly transforming mass into energy.

In the 20th century, famed scientist Albert Einstein added general relativity to the mix. According to the famous theory, space-time is relative depending on one's frame of reference.

The new fixed number is the best estimate of the original expression, Klioner said.

"If we would decide to continue with the old definition, we would have to add several additional conventions to make the latter meaningful in the framework of general relativity," he explained. "A better way was to change the definition completely — and this is what we succeeded in doing."

Capitaine said, "The change of definition of the astronomical unit mainly concerns those in the field of high-accuracy solar system dynamics."

Satellites and other crafts traveling in space are not affected, because they rely on set distances.

"The distance between the Earth and the sun, as any physical distance, should be measured and cannot be fixed by any sort of resolution," Klioner said.

The times, they are a-changing

Capitaine and Klioner are among several scientists who worked over the last two decades on a revision of the astronomical unit. Capitaine said she first got involved when she gave a presentation in 1994 with Bernard Guinot, also of Paris Observatory. Over the course of 10 years, several published papers by various scientists discussed the ramifications of changing the stalwart unit. The three scientists presented the issue to the astronomical community on a number of different occasions.

Other astronomers helped to demonstrate the feasibility of the change before it landed on the table of one of the working groups for the International Astronomical Union. The resolution was reworked several times before it won unanimous passage.

"The change as we have it now is really a product of collective work," Klioner said.

He went on to add, "I think that the energy, commitment, and the worldwide scientific reputation of Nicole Capitaine were crucial for getting this change through."

Shifting from a constantly changing value to a fixed number may seem like an easy choice, but the group faced some resistance. Some believed that the overhaul would be too difficult to implement with crucial software, while others were concerned that discrepancies might be introduced into past work. Still others were uncomfortable changing such a historic definition. Eventually, all concerns were apparently met.
"Within the last two years, I have not heard a single objection for the change itself," Klioner said.

Editor's note: This story has been corrected to fix a units error in the tenth paragraph that incorrectly stated the Earth-sun distance was nearly 150 million meters. It is nearly 150 billion meters.


Earth-Sun Distance Measurement Redefined

One of the stalwart units of astronomy just got a makeover. The International Astronomical Union, the authority on astronomical constants, has voted unanimously to redefine the astronomical unit, the conventional unit of length based on the distance between the Earth and the sun.

"The new definition is much simpler than the old one," says Sergei Klioner of the Technical University of Dresden in Germany, one of a group of scientists who worked decades toward the change, which took effect last month during an IAU meeting

Under the new definition, the astronomical unit (or AU) the measurement used for the Earth-sun distance — is no longer always in flux, depending on the length of a day and other changing factors. It is now a fixed number: 149,597,870,700 meters, which is the equivalent of almost 92.956 million miles.

Klioner explained the simpler definition is helpful, for instance, for scientists who formulate ephemerides — tables that give the precise position of astronomical objects in the sky. They utilize the astronomical unit to calculate the motion of bodies in the solar system. [Solar System Explained From the Inside Out (Infographic)]

"The broader community of astronomers are able now to better, with less efforts, understand what their colleagues — astronomers who are experts in planetary ephemerides — do and how they produce the high-accuracy theories of motion in the solar system," he told SPACE.com by email.

The revision also makes the unit easier for engineers, software designers and students to understand, Klioner and his colleague Nicole Capitaine, of Paris Observatory, noted.

At the same time, the redefinition can serves an epitaph to the bygone era when Earth-bound scientists depended on viewing angles to calculate celestial distances.

An established unit

Lacking precise instrumentation, early astronomers relied heavily on angles to calculate the size of the universe. By studying Mars from two separate points on Earth, 17th-century Italian astronomer Giovanni Cassini was able to use trigonometry to calculate the distance from Earth to the sun with only about a 6 percent error.

"Expressing distances in the astronomical unit allowed astronomers to overcome the difficulty of measuring distances in some physical unit," Capitaine told SPACE.com by email. "Such a practice was useful for many years, because astronomers were not able to make distance measurements in the solar system as precisely as they could measure angles."

Modern instruments can come within a few meters of exactly determining distances of over 150 million meters, or some 93,000 miles.

The astronomical unit eventually came to be defined by a mathematical expression that involved the mass of the sun, the length of a day, and a fixed number known as the Gaussian gravitational constant. Because the Earth orbits its star in an ellipse rather than a circle, the length of a day shifts over the course of a year. At the same time, the sun is constantly transforming mass into energy.

In the 20th century, famed scientist Albert Einstein added general relativity to the mix. According to the famous theory, space-time is relative depending on one's frame of reference.

The new fixed number is the best estimate of the original expression, Klioner said.

"If we would decide to continue with the old definition, we would have to add several additional conventions to make the latter meaningful in the framework of general relativity," he explained. "A better way was to change the definition completely — and this is what we succeeded in doing."

Capitaine said, "The change of definition of the astronomical unit mainly concerns those in the field of high-accuracy solar system dynamics."

Satellites and other crafts traveling in space are not affected, because they rely on set distances.

"The distance between the Earth and the sun, as any physical distance, should be measured and cannot be fixed by any sort of resolution," Klioner said.

The times, they are a-changing

Capitaine and Klioner are among several scientists who worked over the last two decades on a revision of the astronomical unit. Capitaine said she first got involved when she gave a presentation in 1994 with Bernard Guinot, also of Paris Observatory. Over the course of 10 years, several published papers by various scientists discussed the ramifications of changing the stalwart unit. The three scientists presented the issue to the astronomical community on a number of different occasions.

Other astronomers helped to demonstrate the feasibility of the change before it landed on the table of one of the working groups for the International Astronomical Union. The resolution was reworked several times before it won unanimous passage.

"The change as we have it now is really a product of collective work," Klioner said.

He went on to add, "I think that the energy, commitment, and the worldwide scientific reputation of Nicole Capitaine were crucial for getting this change through."

Shifting from a constantly changing value to a fixed number may seem like an easy choice, but the group faced some resistance. Some believed that the overhaul would be too difficult to implement with crucial software, while others were concerned that discrepancies might be introduced into past work. Still others were uncomfortable changing such a historic definition. Eventually, all concerns were apparently met.
"Within the last two years, I have not heard a single objection for the change itself," Klioner said.


Measuring The Diameter Of The Sun, A Science Activity

OVERVIEW: The earth is approximately 150,000,000 km from the sun. This distance varies somewhat with the seasons because of Earth's elliptical orbit. Yet, a simple instrument can be constructed which will provide measurement data that permits a relatively accurate measurement of the sun's diameter.

The relationship that will be used is:

From this relationship we can derive a formula:

2 small cardboard boxes--size not critical but should be ridged enough to hold their shape well

2 pieces stiff cardboard 10 cm X 20 cm (perhaps from a shoebox)

single edged razor blade or sharp knife

small piece of aluminum foil

ACTIVITIES AND PROCEDURES:

1. Tape the lids of the boxes shut securely. Cut slits in opposite sides of each box, directly opposite each other. Make each slit in the form of a capitol "I" and of a size that will fit the meter stick snugly when the box is pushed on to the meter stick. If measurements and cuts are made carefully the face of the box will be perpendicular to the meter stick. This is important. Tape one box securely near one end of the meter stick but leave the other box free to slide.

2. Cut a 5 cm X 5 cm hole near one end of one piece of cardboard and cover with the aluminum foil. Tape the foil in place. Punch a very small hole near the center of the foil with a sharpened pencil lead or a pin.

3. Tape this card to the box that has been secured to the meter stick.

4. Draw two parallel lines exactly 8.0 mm apart near the center of the remaining cardboard.

5. Tape the card with the parallel lines to the face of the sliding box. Note: Be certain both cards are as nearly perpendicular to the meter stick as is reasonably possible. The lines are perpendicular to the meter stick.

6. Point the end of the meter stick that holds the foil-covered card toward the sun. CAUTION: Do not look at the sun! Move the meter stick around until the shadow of the foil-covered card falls on the other card. A bright image of the sun will appear on the sliding card. Move the sliding card until the bright image of the sun exactly fills the distance between the parallel lines. Measure the distance between the cards on the meter stick. Distance between the two cards = mm.

7. Use the formula from the theory section to calculate the diameter of the sun. Use 150,000,000 km as the distance from Earth to the sun.

8. Find the percent difference between your measurement of the sun's diameter and the accepted actual diameter of the sun which is 1,391,000 km.

List factors which could account for the difference between your measurement and the accepted diameter of the sun.

The calculation you made in step 8 was a test of measurement ACCURACY. What could you do to test the PRECISION of your meter stick instrument?

FOR FURTHER STUDY: The actual distance between the earth and sun varies from a minimum of 147,097,000 km to a maximum of 152,086,000 km.

1. Recalculate the diameter of the sun using your distance between cards measurement and the minimum distance between the earth and sun in the formula.

2. Again, recalculate the diameter of the sun using your distance between cards measurement and the maximum distance between the earth and sun in the formula.

3. Does the accepted actual diameter of the sun fall between your calculations B and C?

How do calculations B and C affect your estimation of the accuracy of your measurement as opposed to the percent difference you calculated in step B above?

Refer to the relationships described in the theory of this lab and derive a formula for calculation the distance from the earth to the sun. Use the measurements you can obtain from your meter stick instrument to calculate this distance. Obtain an astronomy reference which gives the actual distance between the earth and sun on a given day or week to check the accuracy of your instrument.

What changes or refinements would you make in your meter stick instrument if you were to plan to chart the earth-sun distance through the remainder of the school year? How could you present the results of such a charting project in a meaningful way?