Mir Marathon

Bruno Tilgner (Bruno_Tilgner@compuserve.com)
Mon, 2 Jun 1997 08:38:26 -0400

There is now a period where Mir is visible at each consecutive
orbit during the night (Leo Barhorst has just reported three such
observations), the reason being that the orbital plane is
approximately parallel to the plane of the terminator.

This can be formulated in somewhat more quantitative terms.

1. The difference between the right ascension of the ascending
   node of Mir and the right ascension of the sun must be 90 deg.

           RAAN - RAsun =3D 90 [deg]

   In reality, the condition is somewhat less stringent. There is
   a small band at either side of 90 deg. =


2. The sun's declination must have a certain minimum value which
   depends on the inclination of the orbital plane and the height
   of the satellite above the earth.

   Assuming a circular orbit of 400 km height and i =3D 51.6 deg,
   a simple calculation will show that the minimum declination
   must be at least 18.6 deg.

These two conditions are met in the northern hemisphere in early
June. Mir is then continuously sunlit. In fact, it entered sunlight
on 31 May at 09:33 UT and stays there until 4 June at 13:47 UT.

The marathon can only be observed from sufficiently high northern
latitudes. At lower latitudes fewer consecutive passes can be
observed because the longitudinal displacement from one orbit to
the next due to the rotation of the earth is too great. At very
high latitudes, on the other hand, Mir does not rise sufficiently
high above the horizon.

How many consecutive orbits can be seen depends thus essentially
on the observer's latitude. The effect of longitude is very small.

The period of continuous sunlight is preceded and followed by several
days with extremely short shadow periods, in the order of a few
minutes. The change is due to the precession of Mir's orbital plane
which is 5 deg per day.

The same phenomenon occurs for the southern hemisphere. The condition =

for the right ascensions is

               RAAN - RAsun =3D -90 [deg]

(again, with a small band), and the declination of the sun must
be below -18.6 deg. This is the case at the end of December.
Mir will enter sunlight on 23 December at 21:56 UT and stay there
until 27 December at 14:14 UT. This is calculated with current
TLE's; the actual times will therefore certainly change somewhat.

However, there is very little land on the southern hemipshere at
suitable latitudes, so the event will probably go by unnoticed.


Similar considerations apply to virtually all satellites in low
earth orbits but become more complex if the orbit is eccentric.

Bruno Tilgner
48.85N 2.02E
100533.2016@compuserve.com=