How is the radius of the Earth determined?

In summary, the value of the Earth's size and shape has been determined through various methods throughout history, with the most accurate model being a combination of data from satellites and astronomical observations. The Earth's size and shape have been a subject of study for many scientists, including Newton, and the determination of the size of the meter has also been closely linked to the Earth's size. Despite the use of the WGS-84 Earth ellipsoid as a reference, it is important to note that it is a mathematical construct and may not accurately represent the Earth's surface. With the advancement of satellite technology, the question of the Earth's size and shape is now easily answered through images from space at a known distance. However, there can still be a margin
  • #1
elevenb
35
1
I was sitting down thinking yesterday, I know that it was worked out through the ages by various methods. But how did we come to the value which we have today? All I can seem to find on the subject is this https://heasarc.gsfc.nasa.gov/docs/cosmic/earth_info.html which says that it is determined by orbiting spacecraft ; does anyone have any links to papers with information on the subject?

Regards,

Mark
 
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  • #2
mc94 said:
I was sitting down thinking yesterday, I know that it was worked out through the ages by various methods. But how did we come to the value which we have today? All I can seem to find on the subject is this https://heasarc.gsfc.nasa.gov/docs/cosmic/earth_info.html which says that it is determined by orbiting spacecraft ; does anyone have any links to papers with information on the subject?

Regards,

Mark

The Greeks did it first!



http://ciese.org/curriculum/noonday/ -- a hands-on project where students reproduce the results of Eratosthenes
 
  • #3
I know who did it first! I'm just wondering how the more accurate measurement that we have today came about?
 
  • #4
Part of the more accurate measurements come from various satellites (several). Part comes from very long baseline interferometry (making measurements from various stars from various locations on the Earth). You're combining a lot of different sources of data. You don't have some single source you could point to. Try the International Earth Rotation Service's website if you want some detail on where the source data for their models come from.

Additionally, your question is rather vague. Do you mean how we came up the most accurate model we have today? Or do you mean the model we use for all of our maps? The answer is different. When the GPS satellite constellation came on line, we started making all of our maps using the same model GPS was using, which was the most accurate model available at that time (WGS-84). Now, if we change to a more current model of the Earth, we have to replace all of our maps. Instead of doing that, we keep on using WGS-84 (albeit a WGS-84 model with constants that were slightly revised in 1996).
 
  • #5
Here is an article on the development of the Earth ellipsoid:

http://en.wikipedia.org/wiki/Earth_ellipsoid#Historical_Earth_ellipsoids

The process of determining the shape of the Earth and its size has occupied many famous scientists over the years including Newton:

http://en.wikipedia.org/wiki/Meridian_arc

Determining the size and shape of the Earth is not a trivial problem. Before satellites, astronomical observations and physical surveys were used to refine the mathematical models scientists developed to characterize the size and shape of the earth. Such work was also involved in the determination of the size of the meter, since one meter was originally defined as 1/10 millionth of the distance on a meridian arc between the north pole and the equator at sea level.

http://en.wikipedia.org/wiki/Metre
 
  • #6
I love the WGS-84 Earth ellipsoid. The highest point on the island of Diego Garcia is about 56 meters below sea level. (They tend to list their elevation relative to the local ocean level, since using the WGS-84 elevation might hurt tourism.)

After Katrina, the elevation of New Orleans (-6ft to 20 ft) was a hot issue. An elevation 6 feet below sea level (-2 meters) is low, to be sure, but it doesn't necessarily mean exactly what people think it means. (More important was the elevation of Lake Ponchartrain and the elevation of the Mississippi River.)
 
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  • #7
BobG said:
I love the WGS-84 Earth ellipsoid. The highest point on the island of Diego Garcia is about 56 meters below sea level. (They tend to list their elevation relative to the local ocean level, since using the WGS-84 elevation might hurt tourism.)

You can book your DG vacation only thru the Uncle Sam Travel Agency (otherwise known as the Department of Defense):

http://en.wikipedia.org/wiki/Diego_Garcia

After Katrina, the elevation of New Orleans (-6ft to 20 ft) was a hot issue. An elevation 6 feet below sea level (-2 meters) is low, to be sure, but it doesn't necessarily mean exactly what people think it means. (More important was the elevation of Lake Pontchartrain and the elevation of the Mississippi River.)

Any resemblance between the geodetic ellipsoid and the Earth's surface is entirely coincidental, since the former is a mathematical construct.

As to New Orleans, even inside the bowl which is enclosed by levees, it was well known (by the locals at least) that there are some areas which are relatively high, and other areas which are relatively low. The French Quarter, one of the oldest parts of the city, was constructed on some of the highest ground (before the levees were built) and thus was spared severe damage from flooding. Other areas of the city were not so fortunate.
 
  • #8
SteamKing said:
You can book your DG vacation only thru the Uncle Sam Travel Agency (otherwise known as the Department of Defense):

Been there, saw the coconut crabs, watched someone get the Queen's chickens drunk on crackers soaked in vodka, swam in the ocean, built some bombs for the U.S. Air Force, got sunburnt, then came home. Oh, and I toured the GEODDS facility they had their. Pretty neat.
 
  • #9
With satellite technology, the question is irrefutably answered by images from space at a known distance, as already suggested by other posters.
 
  • #10
Chronos said:
With satellite technology, the question is irrefutably answered by images from space at a known distance, as already suggested by other posters.
(bolding mine)

Uh, oh. How did they know that distance?

It amazes me that a hundredth of a degree of error in a tracking antenna's measurements means up to about a 7 km error in position for a geosynchronous satellite, and that on many antennas, there's no attempt to correct antenna errors unless they're greater than 3 hundredths of a degree (which would be up to 21 km error), and then we don't really start to panic about two satellites being too close together unless they're within 5 km of each other. Obviously, we can use a statistical analysis (a least squares determination method) and a lot of observations to weed out most of the errors and determine satellites' positions a lot more accurately than the mechanical tools we're using could with a single observation. But you do realize that, at least at first glance, you're essentially saying that you're measuring your position from a "known" object whose position you measured from your "known" position.

There's never a straight forward, obvious answer like "from a known distance" since it isn't easy to know any distances for objects in space.

The history of the term "astronomical unit" is a good example. If we knew how far away the Earth was from the Sun, then we'd know how far all of the other planets were away from the Sun (thanks to Kepler's third law). The problem was figuring out a way to determine how far away the Earth was from the Sun. So we measured the planets' distances from the Sun in "astronomical units". Don't know how long an astronomical unit is, but Jupiter is 5.2 (or so) of them away from the Sun.

The book, "Chasing Venus" by Andrea Wulf, tells the story of the world's first international science project: observing the transit of Venus from as many different spots on the Earth as possible in order to figure out just how long an astronomical unit was.

Some of the stories about how our current "known distances" were determined are just amazing.
 

1. How do scientists measure the radius of the Earth?

Scientists use a variety of methods to measure the radius of the Earth, including satellite imagery, triangulation, and measuring the curvature of the Earth’s surface. One of the most accurate methods is using satellite data and precise mathematical calculations.

2. What is the current accepted value for the radius of the Earth?

The current accepted value for the radius of the Earth is approximately 6,371 kilometers (3,959 miles). This value is based on extensive measurements and calculations by scientists over the years.

3. How accurate is the measurement of the Earth's radius?

The measurement of the Earth’s radius is considered to be very accurate, with a margin of error of less than 0.3%. This accuracy is due to advancements in technology and the use of multiple methods for measurement.

4. Has the radius of the Earth changed over time?

The radius of the Earth has not changed significantly over time. While there may be slight variations due to natural processes such as tectonic movement, these changes are very small and do not significantly impact the overall measurement of the Earth’s radius.

5. Why is it important to accurately determine the radius of the Earth?

Knowing the accurate radius of the Earth is crucial for a variety of scientific and practical purposes, such as mapping, navigation, and understanding the Earth’s gravitational pull. It also helps us gain a better understanding of our planet and its place in the universe.

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