Celestial mechanics planetary positions, using geometrical or arithmetical techniques, and contemporary discussions of the physical causes of the planets' motion. Johannes Kepler (1571–1630) was the first to closely integrate the predictive geometrical astronomy, which had been dominant from Ptolemy in the 2nd century to Copernicus, with physical concepts to produce a "New Astronomy, Based upon Causes, or Celestial Physics" in 1609. His work led to the modern laws of planetary orbits, which he developed using his physical principles and the planetary observations made by Tycho Brahe. Kepler's model greatly improved the accuracy of predictions of planetary motion, years before Isaac Newton developed
Stellar halo be investigated in much more detail; this data has been used to postulate a triaxial or oblate halo. More recent studies have found the halo to be flattened with a broken power law radius dependence; evidence for triaxiality is unclear. As a result of their faint brightness, observations of stellar halos in distant galaxies have required very long exposure times, the stacking of data from numerous galaxies to obtain averaged properties, or observing only the resolved stellar populations. Individual resolved stars in stellar halos can only be measured in the Milky Way and Andromeda. The furthest stellar halos detected are