TO: FM4/Chief, Mathematical Physics Branch

FROM: FM1/Assistant Chief, Mission Planning and Analysis Division

DATE: May 27 1966

66-FM1-64

SUBJECT: CSM orbit determination using the LEM radar

Apparently it is planned to use the LEM radar while that spacecraft is sitting on the lunar surface to determine the CSM's orbit. I am told that the radar angle data accuracy is so poor it will not even be used; the command module's orbit determination will be carried out with range and range rate observations. Considering the extremely slow rotational rate of the moon, I cannot for the life of me understand how it will be possible to accurately determine the orientation of the command module's orbital plane. I am told they intend to do this after the command module has made a plane change, which occurs a couple of orbits before LEM ascent, and the results will be used to establish orbital insertion conditions for the LEM launch targetting.

Could you analyze the situation, determining how well the various orbital elements m_y be determined for the following data gathering periods: (a) one-half pass, starting from horizon to directly overhead, (b) one complete pass from horizon to horizon, and (c) two complete passes from horizon to horizon. I am also interested in being informed about the correlation of the various orbital elements; for example, orbital period and orientation of the plane.

I may have this all messed up and perhaps they do not really intend to do the things in the way I understand it, but I certainly would appreciate it if you would make a rather abbreviated, order of magnitude type, analysis of this within the next couple of weeks in order to determine whether it is even reasonable to include such a program in the LEM computer or alternatively if it mnst be modified to make it insensitive to small bias and random errors in the radar data. I just can't help comparing this to a single radar station on the ground where conditions are far superior and our results are not red hot.

Howard W. Tindall, Jr.