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This answer to Do antennae on the ISS have to constantly move to maintain data links? discusses some of the challenges precisely pointing an antenna mounted to the ISS exterior. While the ISSs orbit and attitude are generally known quite well and probably available those are global parameters and the ISS structure will flex under differential heating as the direction of the Sun is continuously changing and frequently eclipsed:

All pretty simple in principle, complicated by the gimbal's own internal dynamics (including friction), and the significant amount of flexibility and vibration of the ISS (including time-varying thermal distortion, which is what drives the need to search for TDRS at the start of each tracking session, as the ISS "bananas" in different directions as it heats up and cools down).

Question: How much does the ISS banana? How much does it bend and flex and twist under the constantly changing conditions of solar heating?

Just for illustration; three points along a structure might nominally fall on a line, but as it bends they could make two line segments that deviate from collinearity by say 0.01 degrees maximum, or an extreme location's position may deviate from its nominal location by 1 cm maximum for example.

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The short answer is, “It doesn’t”. But this only applies to antennae mounted to the modules. The long answer, which applies to antennae mounted on the truss, “Lots, in complicated ways. But those steely eyed missile men have a handle on it. ”

The ISS structure can be simplistically modeled as a crucifix formed by the truss and the modules.

The modules can be modeled as a cylindrical aluminum pressure hull from Zvezda to Harmony. This aluminum tube is surrounded by interrupted sausage links of MLI insulation jacket. If one side of the tube were a different temperature than the other, the geometry of the tube and the expansion coefficient of aluminum could be used to calculate the “banana bend”. However, this hypothetical aluminum tube is held at constant shirtsleeve temperature by the External Active Thermal Control System (EATCS). There is net cooling, but localized resistance heating is also used to prevent condensation. The “sausage link” insulation would change temperature, but insulation sections are not structurally connected. Therefore, to a first approximation, the ISS modules do not suffer from thermal banana stresses.

It would be fascinating to have crew mount a laser pointer so it shines down the axis. The banana bend could be measured directly at the midpoint with a tape measure.

The Integrated Truss Structure is much more complicated. It is constructed of dissimilar metals (steel, titanium and aluminum) with Kevlar micrometeor armor (which also provides shading). It also has components of the EATCS, which cool power distribution electronics on the S0, S1 and P1 truss segments.

This NASA paper https://ntrs.nasa.gov/api/citations/19910001728/downloads/19910001728.pdf models thermal distortion in a simple box truss spacecraft. It showed significant pointing errors for antennae at opposite ends of the truss. Pointing errors were mitigated with thermal enclosure of the truss (like the Kevlar armor panels on the ISS truss).

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    $\begingroup$ The short answer is, “It doesn’t” - Citation needed $\endgroup$ Nov 9, 2021 at 18:02
  • $\begingroup$ The short answer applies to antenae mounted to the modules, as in the included explanation of lack of thermal stress in the module section. No stress, no aiming error. The long answer applies to antennae mounted to the truss $\endgroup$
    – Woody
    Nov 9, 2021 at 18:14
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    $\begingroup$ You've presented some theories on what you think happens. "In God we trust, all others bring data" - MOD motto. $\endgroup$ Nov 9, 2021 at 18:17
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    $\begingroup$ Yes, S1 and P1 are part of the ITS. In terms of "banana flexing" from thermal loads, they are closer to the center of the truss, S0. Angular antenna misalignment from Banana-ing will increase in proportion to the distance from the center of ITS. S6 and P6 will have the most misalignment if displacement is uniformly distributed along ITS. However, this is a moot point since there are no antennas outboard of S1 and P1. Should have written, "not on the peripheral ITS". $\endgroup$
    – Woody
    Nov 10, 2021 at 5:40
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    $\begingroup$ There's no Kevlar on the truss structure. The truss shroud is only made from Beta cloth. Source: I do MMOD work for ISS. $\endgroup$
    – Tristan
    Nov 12, 2021 at 18:51

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