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@karthikeyan's excellent answer links to The Rotation and Interior Structure Experiment on the InSight Mission to Mars (Folkner, W.M., Dehant, V., Le Maistre, S. et al. Space Sci Rev (2018) 214: 100. https://doi.org/10.1007/s11214-018-0530-5), and includes this image from there.

The antennas need to point towards Earth when InSight is near the edge of Mars' disk as seen from Earth so that the Doppler shift of the returned signal will be sensitive to small changes in Mars' rotation. The antennas are back-to-back so that the signals will be received and rebroadcast coherently both when moving towards Earth and away from Earth, corresponding to the East-pointing and West-pointing antenna, respectively.

This will need to be done over a period of at least two years in order to get a sufficient amount of data to detect the very tiny changes in Mars' rotation due to things like the polar caps evaporating and re-forming for example.

Considering all of this, I can't understand why it looks like the two horn antennas have been rotated slightly clockwise as viewed from above, slightly south of east, and north of west. Why exactly?

enter image description here

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    $\begingroup$ Exact details from the paper will be as follows :"One antenna points 15.5◦ south of due east and the other point 6◦ north of due west. These angles were designed to provide good viewing geometry for RISE while also allowing low-rate telemetry from Earth to the lander throughout the mission". Still the why question remains unanswered $\endgroup$ – karthikeyan Nov 24 '18 at 6:03
  • $\begingroup$ @karthikeyan wow, the plot thickens. That's quite interesting. $\endgroup$ – uhoh Nov 24 '18 at 6:15
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    $\begingroup$ There's also the 25° tilt of Mars axis that changes the pointing direction of antennas throughout the year. The opening angle of the antennas might not be as large as the required 50°. $\endgroup$ – asdfex Nov 24 '18 at 14:12
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    $\begingroup$ @uhoh I just checked the paper. There are no references to the angle numbers! $\endgroup$ – karthikeyan Nov 24 '18 at 18:20

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