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## Introduction

Hundreds of artificial satellites orbiting the Earth can be seen with modest observing equipment. Many of these satellites do not have a constant brightness; they give off flashes at (usually) regular times. This flashing behavior is caused by the rotation of the satellite around its rotation axis. The satellite's metallic surfaces periodically act as mirrors for the sun (specular reflection). Objects with a diffusely reflecting surface will also show varying brightness since the observer will see a changing amount of light reflecting area of the rocket as it tumbles about in its orbit.

In some cases payloads will turn around an axis (e.g. for stabilization purposes, or when they are out of control after their useful life) and show specular reflections. Polished extensions, such as antennas or solar panels periodically act as mirrors, and cause bright flashes, which can reach negative magnitudes. Payloads only occasionally give off regular flashes.

Rocket bodies (third stages) can receive a little kick during insertion of the payload into orbit and can start to tumble around one or more axes. Depending on the reflectivity of the surfaces, rockets can give off specular or diffuse flashes. Third stages usually give off quite regular flashes, due to the simplicity and symmetry of their construction.

Fragments (space debris) are brought into orbit in an uncontrolled way and usually show some rotation. Though fragments occasionally give off regular flashes, these flashes cannot be interpreted because most fragments are irregularly shaped.

Observing a (semi) regularly flashing object (payload or more likely third stage) and measuring the time between two flashes or maxima/minima in the light curve can provide an estimate for the satellite's rotation period (or half of it). This estimate is not perfect since the satellite's motion with respect to the observer introduces a synodic effect, which causes differences between the flash period and the rotation period. The flash period is the time between two flashes as seen by the observer, the rotation period is the time the rocket needs to turn around its axis once. One can use the synodic effect to one's advantage by measuring the time of all flashes seen during one pass and using these measurements to extract information about the direction of the rotation axis.

Below we present a new method to determine the rotation axis of an object of which the rotation axis is perpendicular to the main reflecting, cylindrical body axis, using time estimates of flashes during one or several satellite passes, obtained by visual observers with manual stopwatches.

The temporal evolution of the direction of the rotation axis of a tumbling satellite can shed light on the torques acting on the satellite. These torques have not all been very well studied, as is demonstrated in the final installment of this series of articles.

Next: Determining the rotation Up: The determination of Previous: Preface

bdp@mpe-garching.mpg.de