As shown in the diagram on the right, the difference between the unlensed angular position \ vec { \ beta } and the observed position \ vec { \ theta } is this deflection angle, reduced by a ratio of distances, described as the lens equation
12.
Other astronomers of the period also made suggestions for obtaining uniform time, including A Danjon ( 1929 ), who suggested in effect that observed positions of the Moon, Sun and planets, when compared with their well-established gravitational ephemerides, could better and more uniformly define and determine time.
13.
The ephemeris second is the duration of time that, when used as the independent variable in the laws of motion that govern the movement of the planets and moons in the solar system, cause the laws of motion to accurately predict the observed positions of solar system bodies.
14.
A study directed by Dr . Douglas N . C . Lin, of the University of California at Santa Cruz, yielded a possible explanation for finding actual planets in such cozy proximity to their stars : they could have formed farther out and then migrated inward to their observed positions.
15.
Rogers, who nurses sick and injured kangaroos back to health at her one-acre ( a half hectare ) sanctuary in Lancaster, Ohio, said the 3-year-old animal could not " posture, " a natural observing position for kangaroos in which they stand on hind legs with their front paws up in the air.
16.
At the time of publication of Hansen's Tables of the Moon in 1857, astronomers generally believed that the lunar theory was at last complete; but within about a decade, it was noticed, and shown by Simon Newcomb, that the optimism had been unfounded : deviations between computed and observed positions began to grow at a rate showing that further refinement was necessary.
17.
This derivation only uses the star's " coordinates " at the time of emission, and therefore has the " formal " advantage there is no place for the relative velocity of the star towards the astronomer and therefore it is evident that the observed position doesn't depend on the star's velocity provided that the resultant change of position is much smaller than the distance between star and Earth.
