The conversation between human and AI assistant.
What is the integral of [math] \sqrt{\cos(2x)} [/math]?
That's interesting. Can you tell me more about how elliptic integrals are used in satellite orbits?
Certainly. In celestial mechanics, elliptic integrals arise in the study of Kepler's laws of planetary motion. The design and analysis of satellite orbits often involve solving differential equations that require the use of elliptic integrals. For example, the problem of determining the position of a satellite in orbit can be reduced to solving an elliptic integral.