Fig 1.

$$ \theta(\nu,t) = \arctan(\frac{S_X \nu t}{Nh}) + \theta_0 $$

Where

• $\theta(\nu,t)$ [rad]: slew of the satellite
• $S_x$ [m]: swath dimensions in the across track spatial dimension
• $\nu$ [s^-1]: frame rate of the sensor
• $N$ [unitless]: number of frames
• $h$ [m]: orbital altitude
• $t$ [s] : time the satellite is on its orbital trajectory
• $\theta_0$ [rad]: the initial slew angle at $t = 0$

Assumptions

• Flat Earth

• The restriction that the swath is square in shape is imposed

• Satellite travels at a constant orbital speed

• Derivation

Reference Sources:

Imaging payload performance considerations for on-orbit servicing and active debris removal.pdf