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Informator Kosmiczny .::Prawo Pięści( Fist law)::.
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.::Prawo Pięści::. „Prawo pięści” to nazwa nowej, niezwykle prostej metody ustalania odległości do przelatujących satelitów opracowanej w naszym obserwatorium. Jedynym potrzebnym narzędziem jest.. nasza własna pięść! Poniżej opis, jaki został zaprezentowany na konferencji GLOBAL HANDS ON UNIVERSE w Paryżu w lipcu 2003. Napisz do nas, jeśli chcesz dostać bardziej dokładną polską wersję ze wzorami i rysunkami (opublikowana w URANII nr 6/2000). FIST
LAW or the simplest method for
obtaining distances to satellites Ludwik
Lehman
II
Liceum Ogolnokształcace in Glogow,
Polska
[Poland]
Abstract: How to obtain (using only your fist) approximate distances to satellites passing the sky above your head.
When you see satellites moving slowly across the sky, you may think how far these shining points are. It seems exceedingly difficult to measure their distances, but as long as you do not need to be very accurate, it is not. What are you able to do looking at a satellite crossing the sky? First, you can estimate the time it needs to draw some angle. Which angle? For example, you can use the fist of your stretched hand which covers approximately 10 degrees. If you measured the time when the satellite was close to its highest altitude, you can now easily obtain its distance from you. How? You need only multiply the crossing time (in seconds) by fifty and the result will be approximately equal to the satellite distance expressed in kilometers. If you prefer to have the distance in miles, multiply the time in seconds by thirty. Let us resume: Satellite distance (in kilometers)
= 50 x crossing time (in seconds) Satellite
distance (in miles) = 30 x crossing time (in seconds) (1) Why
does it work? The distance made by a satellite during a given time can
be expressed by a wellknown formula: Distance
made by the satellite = velocity x time
(2) We
know that most of satellites are moving around the Earth in almost
circular orbits. There is only one velocity that a satellite can have in
order to remain in a circular orbit with a fixed radius. The velocity
depends on the radius of the orbit, so the satellites moving on
different orbits have different velocities. Since the orbit radii for
the loworbit satellites are almost the same, this dependence is not
very strong. Let
us assume that without binoculars we are able to observe satellites that
are not farther than 1000 km (600 miles). The velocity which has a
satellite moving 1000 km above the surface of the Earth equals 7.36
km/s. On the other hand, such the velocity for a satellite, which passes
only 100 km over the Earth surface, equals 7.86 km/s. We see that
despite the tenfold change of the distance from a satellite to the Earth,
the velocity has changed only by about 7%. Thus, we can put the mean
value of the satellite velocity into formula (2) without a considerable
loss of the accuracy. Moreover, the velocity of the observer due to the
rotation of the Earth can be neglected, because it can reach only a few
percent of the satellite velocity. Now, if we denote the angle covered
by a fist of a stretched hand as a,
we can write: Tana=distance
made by the satellite/distance from the satellite to observer (3)
Then
from (2) and (3) we easily get
Distance
from the satellite to the observer = velocity x time / tana
(4) If
we put the average velocity of the satellites in low orbits and tangens
of 10 degrees in formula (4), we get approximately the formula (1). This
''fist law'' is not, of course, very precise. But you need only loudly
count the seconds when a satellite passes your fist in a stretched hand,
and will soon know whether the satellite is 100, 300 or 600 miles from
you. For most of the skywatchers it is really enough. If you want to be
more precise, you can try to measure the time by stopwatch and better
determine the angle covered by your own fist. In this way you will find
your personal formula for obtaining the distances to the satellites.
There are some other ways to do this even more precisely, but this is
another story.

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