In order to determine the shape of Earth, you had to measure the absolute distance between two latitudes (measured in degrees by astronomical means) to determine the size of a latitude degree. These measurements have to be done both close to the Equator as well as close to the Pole.
This was first done by the French Geodesic Mission
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with one expedition sent to current Ecuador, while the "polar" expedition was sent into the Torne river valley in Lapland led by Pierre Maupertuis.
There would be problems with the mechanical support, thermal expansion and hygroscopic effects with such huge boards.
The only use I can think of for such huge boards would be some (micro)stripline filters and transmission lines for VHF or lower UHF and perhaps for constructing large patch antennas with some active electronics integrated between the patches.
So, because of that, you quoted 4140 unnecessary characters, wasted our time having to scroll past them and figure out what you actually were replying to, and also wasted who knows how much bandwidth to download it and local storage to look at it?
How many copies of your message do you figure have been made?
That was the one whose name escaped me, and had a very interesting story from starting off spending the expedition's money on a hooker in the West Indies...
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Paul Carpenter | paul@pcserviceselectronics.co.uk
PC Services
Sounds like people had not done their research as the shape of the Earth mattered to map makers, and navigation long before rockets.
Re-inventing the wheel, and putting a marketing spin on why things went wrong.
Does not sound good to me, but typical of large projects based on technology 'silver bullet' blindness, without fully researching and understanding the problems.
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Paul Carpenter | paul@pcserviceselectronics.co.uk
PC Services
The geoid (the equipotential water level assuming no tide or wind effects) differs about +/-100 m from the reference ellipsoid
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This variation of the gravitational field would attract the rocket during the whole trajectory, causing some deviation from the expected target.
I don't see how these gravitational variations could be mapped accurately before orbiting satellites (by measuring their deviation from the theoretical orbit).
On the Moon, the mascons (mass concentrations) cause so much gravtiy field anomaly that a lunar satellite will crash to the Moon within months or a year, unless active orbital corrections are made.
If you measure the distance between two points and the angle of that short line repeatedly, you can produce a measure of a curve. The distance measurement can be done with survey methods of triangulation. The angle measurement can be done by sighting stars.
I remember hearing that story decades ago. However, looking at the current maps showing the difference between the geoid and the reference ellipsoid, it is hard to think about pear.
To be pear-shaped, there would have to be a deep depression at Antarctica, which does not exist, according to current measurements.
Looking only at geometry, a bulge before or around the target would cause a premature impact point only if the missile approached the target in a _very_ shallow angle. A 100 m bulge and 3 degree approach angle (e.g. airport ILS approach) would cause an impact 2 km prematurely.
In my understanding the ballistic missiles of those days approached the target nearly vertically, so the bulge would affect the impact point only a few meters, although the impact would happen perhaps 100 ms earlier than calculated.
The reason for the "bulge" is that the mass below the Earth's surface is not evenly distributed, i.e. there are low density materials (and hence less mass and less gravitation) below the bulges. The varying gravitational force along the whole flight path will cause deviations in the flight path of the missile.
This is exactly what the French Geodesic Mission did in the 18th century :-). However, you can only determine the diameter of the Earth measured on the equator and on the poles, but you can not map local variations in the gravitational field by that method.
Fortunately the two triangulation networks used by the FGM (one in Ecuador and the other in Scandinavia) happened to be on two separate "bulges", compensating for some of the errors. However, if one network had been on a bulge and the other in a depression, the error would have been larger.
If you only perform these measurements over small distances, or only have limited accuracy, you only end up with the parameters for a spheroid which fits the region being surveyed.
This is why you have multiple geodetic datums (for whatever reason, no-one uses the latin plural "data" in this context), each of which provides a spheroidal approximation to the geoid which is a close fit for a specific area.
The following diagram shows the location of a specific coordinate in a variety of datums:
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[The Tokyo datum is so far out as Japan lies on a relatively steep slope in the geoid, so the best-fit ellipsoid to that area is rather skewed.]
Tying these together requires surveying large areas with a high degree of accuracy. The first major attempts at tying regional datums together were the traverses conducted using the SHORAN and HIRAN distance measuring systems starting in the 1950s.
Obtaining this level of accuracy over long distances simply wasn't feasible until quite recently.
I do. You should read up about them, before commenting to the net. CF is Continued Fraction obviously.
It is highly advisable to understand CF's before attempting approximation programs. I doubt the c-program takes advantage.
Striking fact about CF's. If you need a value to N digits, there is an approximation A/B where both A and B are limited to N/2 digits.
This has an application in 1 bit D/A converters. With 16 bit timers you can have a 32 bit precision average DC output for any value. (Provided your clock is jitter free enough to accomodate this.) (Oops giving away a patent ...)
Groetjes Albert
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Albert van der Horst, UTRECHT,THE NETHERLANDS
Economic growth -- being exponential -- ultimately falters.
You obviously didn't read either the ratapprx program or my message. The uncertainty was about "what you mean". Note the 'you'. ratapprx doesn't do approximations, it does exact calculations (within the limits of the floating point system). Each answer is the next best approximation with a larger numerator. Thus no need of convergents.
I saw no sign of continued fractions. I saw no need of approximations. Thus I asked questions and avoided snotty comments.
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[mail]: Chuck F (cbfalconer at maineline dot net)
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