Student Manual PAGE 4 Equipment Sky and Telescope Reprint LE 11, pocket calculator, IBM-compatible computer running CLEA software for Radar Measurement of the Rotation Rate of Mercury. Introduction Because Mercury is a small planet whose surface features have low contrast, and because it is so close to the sun that it is rarely visible against a dark sky, it is difficult to determine how fast it is rotating merely by looking at it from the earth.  In recent years, however, radar techniques have proven most effective in measuring its speed of rotation.  The method you will employ here actually has wider application than just the measuring the rotation of Mercury.  It can be used to study the behavior of other planets as well, from cloud-covered Venus to the rings of the major planets, to the smallest aster- oids. The technique of this lab is described below and in Reprint LE 11 by Hoff and Schmidt.  The basic idea is to use a radio telescope to send short pulse of electromagnetic radiation of known frequency towards the planet Mercury and then to record the spectrum (frequency versus intensity) of the returning echo.  Depending on the relative position of the earth and Mercury, the pulse will take between 10 minutes and half hour to travel to Mercury, bounce off, and return. By the time the pulse has reached Mercury, it has spread out to cover the entire planet.  Because the planet’s surface is a sphere, the pulse hits different parts of the planet at different times, however.  The pulse first hits the surface at a point directly on a line between the centers of the earth and Mercury (the “sub-radar point”), and few microseconds later from points further back, toward the edges of the planet.  Thus we wait for the first echo, from the sub-radar point, and then by looking at the returning echoes at succeeding times, each a few microseconds later than the next, we get information about different parts of Mercury’s surface. The frequencies of the returning echoes are different from the frequency of the pulse sent out because the echoes have bounced off the moving surface of Mercury.  Any time a source of radiation is moving radially (towards or away from the observer) there will be a Doppler shift in the received frequency that is proportional to the velocity along the line of sight. Figure 1 THE DOPPLER SHIFT