Earth Avoidance Analysis

In order to get accurate attitude updates from the star tracker, it must not point at significantly large and bright objects like the Sun and Earth. Rocket Lab has demonstrated use with the Moon in view, so it can safely be ignored. LISSA's star tracker also points perpendicular to the main solar array, so the Sun will be around 90 degrees from the star tracker's boresight during nominal ram-pointing operations. The only concern remaining is the Earth limb. Due to LISSA's geometry, the star tracker's boresight will point in the anti-ram direction during nominal operations when the payload imager is facing ram. The star tracker has a sun-avoidance angle of 34 degrees, which also applies to the Earth limb, so first we must see if this interferes while the star tracker is pointing anti-ram. The simplified geometry for this problem is shown in the figure below.

In this figure, R is the radius of Earth, which is assumed to be circular. LISSA's position is chosen to be over the North pole for convenience, with A representing LISSA's altitude. From here, we can choose points on Earth's surface by changing φ, calculate the error vector between that point and LISSA given as L, and find the angle θ this vector makes with the star tracker's boresight. This angle should exceed 34 degrees for any point chosen on Earth to guarantee star tracker function while it points anti-ram.

Unfortunately, the Earth limb will be within this avoidance angle. The minimum angle between the Earth limb and the boresight is about 22.2 degrees, 11.8 degrees within the avoidance angle. This requires the star tracker be mounted at a cant angle to avoid the Earth limb while the payload points ram, ideally with a margin that allows some margin to pitch the star tracker towards Earth. The biggest constraint for this was found to be with the spaceraft's structure. The spacecraft's overall envelope would be too large for the CubeSat deployer if the star tracker cant angle exceeded 20 degrees, so 20 degrees was chosen. This cant angle can be seen below.

This cant angle allows for about 8 degrees of pitch toward the Earth before star tracker measurements are affected.