Noted Planet X sceptic Brian G . Marsden of the Minor Planet Center pointed out that these discrepancies were a hundredth the size of those noticed by Le Verrier, and could easily be due to observational error.
12.
In applied statistics, "'total least squares "'is a type of errors-in-variables regression, a least squares data modeling technique in which observational errors on both dependent and independent variables are taken into account.
13.
Mel�ndez & Ram�rez ( 2007 ) have suggested that HD 98618 be considered a " quasi solar twin ", since they have now identified a solar twin, 56948, with lithium content identical within the observational error to the Sun's.
14.
This does not necessarily imply that these reports were a result of observational error, as it is possible that outgassing events on the lunar surface might not leave a visible marker, but neither is it encouraging for the hypothesis that these were authentic lunar phenomena.
15.
Both Newtonian mechanics and general relativity predicted a precession of Mercury's orbit-the difference was that the Newtonian prediction of the rate of precession did not agree with the observed value, whereas the GR prediction did agree ( within the limits of observational error )-see Tests of general relativity.
16.
Although Aristarchus'results were incorrect due to observational errors, they were based on correct geometric principles of parallax, and became the basis for estimates of the size of the Solar System for almost 2000 years, until the transit of Venus was correctly observed in 1761 and 1769 . This method was proposed by Edmond Halley in 1716, although he did not live to see the results.
17.
From the time of Hipparchus and Ptolemy, the year was based on two equinoxes ( or two solstices ) a number of years apart, to average out both observational errors and the effects of nutation ( periodic motions of the axis of rotation of the earth, the main cycle being 18.6 years ) and the movement of the Sun caused by the gravitational pull of the planets.
18.
Though 18 Scorpii is only slightly more metal-rich overall than the Sun, its lithium abundance is about three times as high; for this reason, Mel�ndez & Ram�rez ( 2007 ) have suggested that 18 Scorpii be called a " quasi solar twin ", reserving the term solar twin for stars ( such as 56948 ) that match the Sun, within the observational errors, for all parameters.
19.
These are just a set of numbers and are easily compared to confirm that two bodies are in different orbits, provided that there's enough data for the orbital elements to be well established . ( Different computations of the orbit for the same body may not produce exactly identical numbers, due to things like perturbations and minor observational errors, but the elements will be close enough to suggest when further investigation is required.
20.
These irregularities or " residuals ", both in the planet's ecliptic longitude and in its distance from the Sun, or radius vector, might be explained by a number of hypotheses : the effect of the Sun's gravity, at such a great distance might differ from Newton's description; or the discrepancies might simply be observational error; or perhaps Uranus was being pulled, or perturbed, by an as-yet undiscovered planet.
