All bodies attract each other with what is called gravitational attraction. This applies to the largest stars as well as the smallest particles of matter.
The force of attraction between two small bodies (or between two spherical bodies of any size) is proportional to the product of their masses and inversely proportional to the square of the distance between their centers. In other words, the closer two bodies are to each other, the greater their mutual attraction. As a result, to stay in orbit, a satellite needs more speed in a low than a high orbit.
Kepler's three laws of planetary motion, which had been derived empirically by Johannes Kepler, were obtained with mathematical rigor as a consequence of Newton's law of universal gravitation in conjunction with his three laws of motion.