Low Earth orbit (LEO) satellite networks are capable of providing wireless connectivity seamlessly and continuously to any part of the world with guaranteed short round-trip propagation delay. As a key part of next generation network (NGN) infrastructure, next generation satellite networks are expected to support a variety of applications with diverse performance requirements. This paper argues that the constellation tomography for the LEO satellite network is a preliminary step for efficient satellite network monitoring and performance promotion. To measure the constellation, a divide-and-conquer mechanism is developed for each parameter estimation by delay probing. The delay measurement is only carried out between two terminals located at the same geographic positions. Performance evaluation on several popular polar LEO constellations proves the accuracy and efficiency of the developed constellation tomography algorithms in divide-and-conquer manner. The geographic position limitation of the delay probing terminals for valid constellation inference is also analyzed in the paper.