In space targets,about 7% of them are manmade satellites;others are space relics or debris.Only rely on sun shining can these targets be detected because all of them do not illuminant themselves.They are so far from the sensor that can be considered as point targets.Mathematics model of un-illuminant space target is set up.Based on classical optical theory the relationships between brightness and dimension and surface characteristic and view angle and distance are analyzed;and the relationships between detection ability of optical sensor and parameters of optics and exposal time are demonstrated based on energy conservation law. In the end the correctness of the model and formula are proved by test, so it can provide reference to optical system design used in space un-illuminant targets detection.