The impact of stellar activity from a Jupiter-sized flare of 10 000 K, considering its position shift on the stellar disc during rotation. Left: effect of the Rotation Angle on S/N. Right: variation in the S/N due to stellar rotation period by setting a total exposure time of 20 000 s. Here, ΔS/N represents the difference between the S/N with and without stellar rotation, while S/N denotes the S/N in the presence of stellar activity without rotations. The dashed blue, red, and yellow lines indicate the S/N of the stellar activity region with different distances from the stellar center (i.e., 0.3, 0.5, and 0.9 R_s) by setting α₀ = β₀, respectively. The solid blue, red, and yellow lines represent $\frac{\text{Δ}S/N}{S/N}$ at the same distances.