Obserwacje (zaćmienia)





Inne obserwacje

Meteory i meteoryty

Zjawiska atmosferyczne

Życie w obserwatorium

Obozy i warsztaty


Rok Astronomii

Przejście Wenus

Cele i sposoby działania

Podstrony uczniów i bywalców

II LO w Głogowie



Presented at Paris conference GLOBAL HOU in 2002


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 well-known 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 low-orbit 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:

Tan(a) = 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 / tan(a)   (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 stop-watch 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.



English version

Hands-on Universe

Webcam Astronomy

Fist Law




Klub Astronomiczny

Głogowski Informator Kosmiczny


Prawo Pięści

Zrozumieć gwiazdy

Użyteczne linki



Borowice w Kudowie


Fizyka w II LO

II Liceum Ogólnokształcące

im. Mikołaja Kopernika w Głogowie


67-200 Głogów, ul. Daszyńskiego 15,

tel. 076 7286530 fax 076 7286531