Simultaneous Earth observations from 2 satellites

Simultaneous co-located observations from two different orbits lead to several advantages (i.e., cross calibration of sensors and a wider range of solar-zenith and sensor look angles). The question was asked how many times per year (on the average) do the sub-satellite points of two satellites simultaneously come within D kilometers of each other?. For the Space Station (altitude: 500 km, inclination: 28 deg) and a Sun synchronous satellite (altitude 705 km, inclination 98.21 deg) the answers are 16, 41 and 82 times per year for encounter distances D of 20, 50, and 100 km espectively. The relationship between encounters per year and distance D is linear. The answers were obtained in two ways: (1) a closed form statistical approach which led to a simple algebraic expression, and (2) a Monte Carlo type computer solution. The largest difference between the two solutions was less than 12%.