De Motu Corporum in Gyrum

De motu corporum in gyrum ("On the motion of bodies in an orbit") is the presumed title of a manuscript by Isaac Newton sent to Edmond Halley in November 1684. It followed a visit by Halley earlier in that year, when Halley had questioned Newton about problems then exercising the minds of Halley and his scientific circle in London, including Sir Christopher Wren and Robert Hooke.

The title of the document is only presumed because the original is now lost. Its contents are inferred from surviving documents, which are two contemporary copies and a draft. Only the draft has the title now used; both copies are without title.

This manuscript (De Motu for short, but not to be confused with several other Newtonian papers carrying titles that start with these words) gave important mathematical derivations relating to the three relations now known as "Kepler's laws". (Before Newton's work, these had not been generally regarded as laws.) Halley reported the communication from Newton to the Royal Society on 10 December 1684 (Old Style). After further encouragement from Halley, Newton went on to develop and write his book Philosophiæ Naturalis Principia Mathematica (commonly known as the Principia) from a nucleus that can be seen in 'De Motu' – of which nearly all of the content also reappears in the Principia.