# How is the radius of the Earth determined?

1. Mar 4, 2015

### elevenb

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

2. Mar 4, 2015

### Quantum Defect

The Greeks did it first!

http://ciese.org/curriculum/noonday/ -- a hands-on project where students reproduce the results of Eratosthenes

3. Mar 4, 2015

### elevenb

I know who did it first! I'm just wondering how the more accurate measurement that we have today came about?

4. Mar 4, 2015

### BobG

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. Mar 4, 2015

### SteamKing

Staff Emeritus
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. Mar 4, 2015

### BobG

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.)

Last edited: Mar 4, 2015
7. Mar 4, 2015

### SteamKing

Staff Emeritus
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

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. Mar 5, 2015

### Drakkith

Staff Emeritus
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. Mar 7, 2015

### Chronos

With satellite technology, the question is irrefutably answered by images from space at a known distance, as already suggested by other posters.

10. Mar 17, 2015

### BobG

(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.