Appendix A

In Chapter 1 the 5-parameter model was introduced. With these parameters the geometry of SS433 can be descibed at any given moment. The precession phase can be derived from the Julian Date as follows: The velocity of the beams can be devided into 3 orthogonal components: the radial velocity, the tangential velocity in right ascension and the tangential velocity in declination. is used for the precession cone inclined towards the observer and for its counterpart. This leads to:

The Doppler shift follows as: with the Lorentz factor

The transverse velocities can be converted into observed proper motions ( and ). To do this the light travel time must be taken into account. Define as the declination of SS433 and the distance to SS433. Then:

Using the above equations it follows that differential light travel time leads to a higher absolute value of the proper motion in the approaching beam () than in the receding countertpart (). With the tangential velocity described as one finds:

The proper motions can be found in two ways. The first method uses a series of maps where one can measure the motion of the object in a time sequence. The second method only needs one map, by fitting the differently curved emission pattern on either side of the core. Assume, for simplicity only, that all parameters except and are known, then and are both fixed projections of . This means that the two proper motions in the last equations are independent functions of and , as long as , and under that restriction they therefore allow both parameters to be measured. Or, one cannot adopt a different distance to SS433 by simply postulating a different velocity.