Re: We do not know the distance of stars
- From: Ken Rode <karode@xxxxxxxxxxxx>
- Date: Wed, 05 Apr 2006 20:29:40 -0400
mccoy@xxxxxxxxxx wrote:
Any simpleton who knows basic surveying techniques knows that
triangulation is used in surveying and, indeed in supposed
determination of star distances. Simply put we do not know how far
stars are.
In land surveying multiple angles are often taken to determine
locations. Such determination is done by numerous locations in and
around the distant object in question. We cannot do that with stars.
We're on this side of the universe and there is no possible way to get
to the other side.
Additionally, consider this:
"In triangulation surveys, a great deal of attention was paid to the
geometric strength of figure of each control configuration (see table
A.15). Generally, an equilateral triangle is considered strong,
whereas triangles with small (less than 10 degrees) angles are
considered relatively weak. Trigonometric functions vary in precision
as the angle varies in magnitude."
[comment: astronomers calculate supposed distances based on triangles
that are less than 1 degrees angles]
"The sines of amll angles (near zero), the cosines of large angles
(near 90degrees) angles are all relatively imprecise. That is, there
are relatively large changes in the values of the trigonometric
functions that result from relatively small changes in angular values."
Relatively imprecise in relation to what? Where is this book getting its
sine and cosine values from? Sine and cosine tables? If so, of course
they're imprecise.
For example, the angular error in 5 seconds for the sine of 10 degrees
is 1/7300, whereas the angular error in 5 seconds for the sine of 20
degrees is 1/15000. and the angular error in 5 seconds for the sine of
80 degrees is 1/234000."
I gotta think that sine and cosine tables are involved here somehow.
Doesn't knowing what the error is imply that we know what the accurate
value is?
"One can see that if sine or cosine functions are used in triangulation
to calculate the triangle side distances, care must be exercised that
the trigonometric fucntion itself isn't contributing errors to the
solution more significant than the specified surveying error limits."
"When all angles and distances are measured for each triangle, the
redundant measurements ensure an accurate solution, and the
configuration strength of figure becomes somewhat less important.
However, given the opportunity, most surveyors still prefer to use
well-balanced triangles and to avoid using the sine and tangent of
small angles and the cosine and tangent of large angles to compoute
control distances."
What follows is a series of computational problems that illustrate
error.
Concludes:
"The foregoing illustrates that the surveyor should either avoid using
weak angles in distance computations, or if weak angles must be used,
they should be measure more precisely than would normally be required.
Also illustrated here is the need for the surveyor to preanalyze the
proposed control survey configuration to determine optimal field
techniques and attendant precision. "
Surveying: Principles and Applications
Kavanah/Bird-1984
"...The strength of the figure is a function of:
"1. The geometric strength of the triangles that make up the network.
Ideally, the triangles should be equilateral"
[comment: impossible to get equilateral triangles for astronomical
work.]
Introduction to Surveying
Anderson/Mikhail 1985
JM
John, what part of "if weak angles must be used, they should be measured
more precisely than would normally be required" did you fail to understand?
.
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