After ascent, we are now in outer space. How does a spacecraft move under the influence of the gravitational forces of the Sun, planets, and moons? This is the question we will deal with in this chapter, and we are pursuing general answers to it. Let us face reality from the start: The details of motions are usually very complicated and can be determined sufficiently accurately only numerically on a computer. This is exactly how real missions are planned. But the goal for us is not numerical accuracy, but to understand the basic behavior of a spacecraft. To achieve this, it suffices to study some crucial cases. The easiest and by far the most important case is the mutual motion of two point-like (a.k.a. ideal) bodies in the gravitational field of each other, the so-called (ideal) two-body problem (2BP), which we study in this chapter, such as the Moon in the gravitational field of the Earth. More complicated cases can often be traced back to the two-body problem by minor simplifications.