A History of the Anomalous
Advance of Mercury’s
Perihelion
Classical Dynamics
Phys 5306
TTU Dr. Myles
Fall 2003
Presented by: W. Lee Powell Jr.
Titius-Bode Law
a = 0.4 + 0.3 x 2n
where a is the semimajor axis in (AU) and the exponent, n,
takes values minus infinity, 1,2,3, ...
Planet
Mercury
Venus
Earth
Mars
Asteroid belt
Jupiter
Saturn
Uranus
n
minus infinity
0
1
2
3
4
5
6
Predicted
0.4
0.7
1
1.6
2.8
5.2
10
19.6
Accepted
0.387
0.723
1
1.524
~2.8
5.204
9.582
19.201
Titius-Bode Law

The first test of the law occurred a few
years later (1781) when William
Herschel discovered Uranus --- at the
distance predicted by the relationship.
Independent Discovery of Neptune

After the discovery of Uranus, it was noticed that
its orbit was not as it should be in accordance
with Newton's laws. It was therefore predicted
that another more distant planet must be
perturbing Uranus' orbit. Neptune was first
observed by Galle and d'Arrest on 1846 Sept 23
very near to the locations independently
predicted by Adams and Le Verrier from
calculations based on the observed positions of
Jupiter, Saturn and Uranus.
Independent Discovery of Neptune

An international dispute arose between the English and French
(though not, apparently between Adams and Le Verrier personally)
over priority and the right to name the new planet; they are now
jointly credited with Neptune's discovery. Subsequent observations
have shown that the orbits calculated by Adams and Le Verrier
diverge from Neptune's actual orbit fairly quickly. Had the search for
the planet taken place a few years earlier or later it would not have
been found anywhere near the predicted location.

More than two centuries earlier, in 1613, Galileo observed Neptune
when it happened to be very near Jupiter, but he thought it was just
a star. On two successive nights he actually noticed that it moved
slightly with respect to another nearby star. But on the subsequent
nights it was out of his field of view. Had he seen it on the previous
few nights Neptune's motion would have been obvious to him. But,
alas, cloudy skies prevented observations on those few critical days.
Urbain Jean Joseph Le Verrier
b. 1811 d. 1877
Urbain Jean Joseph Le Verrier
Urbain Le Verrier was appointed to teach
astronomy at the École Polytechnique in 1837
and abandoned his first subject of chemistry. He
worked at the Paris Observatory for most of his
life where his drive for efficiency was to made
him very unpopular. A contemporary said of him:
I do not know whether M. Le Verrier is
actually the most detestable man in France, but I
am quite certain that he is the most detested.
Independent Discovery of Neptune
Le Verrier was a co-predictor of
the existence and position of
Neptune, along with J.C.
Adams.
Le Verrier was better served by
the German astronomer Galle
(who found the planet in one
hour) than Adams was by Airy
who gave the task to Challis,
the director of the Cambridge
Observatory. He observed the
planet first but did not recognize
it.
Urbain Jean Joseph Le Verrier
Le Verrier calculated the position of
Neptune from irregularities in Uranus's
orbit. As one of his colleagues said:... he discovered a star with the tip of his
pen, without any instruments other than
the strength of his calculations alone.

Urbain Jean Joseph Le Verrier



Arago, the director of the Paris observatory who had first
suggested that Le Verrier work on this problem, said
In the eyes of all impartial men, this discovery will remain
one of the most magnificent triumphs of theoretical
astronomy, one of the glories of the Académie and one
of the most beautiful distinctions of our country.
Le Verrier received many honours and widespread
recognition for this achievement. The London Times
carried the headline on the 1 October 1846:Le Verrier's planet found.
He was awarded the Copley Medal of the Royal Society
of London and, in France, became an officer in the
Legion of Honour.
Urbain Jean Joseph Le Verrier

In 1854 Le Verrier became director of the
Paris Observatory but his unpopularity,
mentioned above, led to him being
removed from the post in 1870. A
successor was appointed but died in 1873.
At this time Le Verrier again was given the
post but his authority was severely
restricted as he was supervised by a
council. He held the post until his death.
Urbain Jean Joseph Le Verrier
 Soon
after arriving at the Paris
Observatory, Arago also suggested
that Le Verrier work on trying to
obtain a solution for the orbit of
Mercury. This project occupied Le
Verrier for much of his life.
Mercury: A Difficult Observing
Target
Nearest planet to the Sun.
 Never more than 28 degrees away from
the Sun.
 Legend says that Copernicus lamented
that he had never seen Mercury himself.

Mercury From Earth
Alignments of Mercury
Mercury Transits
Transits provide very accurate
measurements of orbital parameters.
 Don’t occur at every inferior conjunction:
so relatively rare (something like 7 years
apart).
 Example: Last three occurred in 1986,
1993, and 1999.

Mercury at Transit
Le Verrier’s Results


Produced the first theory of Mercury’s orbit in
1843. Not perfect, since it was based mostly on
older observations.
Reworked theory using most recent and
accurate observations, resulting in a revised
theory, published in 1859, including the
discovery of an anomalous advance in the
perihelion: the cause of the discrepancy
between prediction and observation.
Mercury’s Perihelion Advance
Anomalous Perihelion Advance
Why wasn’t it discovered previously? Its
size!
 To be clear: “Anomalous” refers not to the
fact that there is an advance, but to the
size of it: it differed from what Newtonian
mechanics predicted based on the known
planetary bodies.

Anomalous Perihelion Advance
Planetary perturbations result in a
predicted advance of a little more than
500” per century.
 Mercury makes about four orbits a year, so
this amounts to around 1 ¼” per orbit.
 260,000 years for a complete precession.

Anomalous Perihelion Advance

Theoretical predictions by Le Verrier, due to
planetary bodies in arcseconds/century:
Venus:
280”.6
Earth:
83”.6
Observed
Mars:
2”.6
amount:
Jupiter:
152”.6
39”/century
Saturn:
7”.2
greater!!
Uranus:
0”.1
TOTAL:
526”.7
Possible Causes?
Le Verrier’s proposed solutions: Two
possibilities:
1) Errors in the estimated masses of
the planets, particularly Venus.
2) An as yet undiscovered planet:
Vulcan!
Vulcan


The name Vulcan had been put forth by Babinet, a
French astronomer with a habit for this type of thing. If
more than one were discovered: the Cyclopes!
Around the same time predicted Hyperion, outside of
Neptune’s orbit, to explain the differences between Le
Verrier’s predicted value, and the actual orbit observed.
Vulcan
 Le
Verrier proposed either a single
planet, several small planets, or even
a disk of material.
 Numerous false identifications, no
definitive discovery.
 Very robust assertion!
Simon Newcomb
1882: American astronomer Newcomb
verified Le Verrier’s theory of the motion of
Mercury.
 1895: Produced detailed work on the
orbits of Mercury, Venus, Earth, and Mars,
which became the basis for the tables of
these planets’ motions in the main national
ephemeris.

Simon Newcomb

His solution: An alteration of Newton’s law
of gravitation. The change made the
tables very accurate, but was abandoned
within just a few years.
Hugo von Seeliger



Director of the Munich observatory from 1882 to
1924.
Next big theory to be accepted: matter
surrounding the Sun, similar to Le Verrier’s
suggestion. He supported the theory with
observations of the zodiacal light.
The zodiacal light appears at dusk or dawn near
the horizon where the Sun just set or will rise:
now accepted to be due to small particles near
the Sun scattering light.
Velocity-dependent Force Laws

Wilhelm Weber, Gauss, Riemann,
Clausius, Ritz, Maxwell…
Finally, Einstein


General Relativity: 1915.
Einstein used Le Verrier’s anomalous advance
of Mercury as a prime application of his theory:
it gave the correct answer!
Einstein
Albert Einstein published his General Theory of
Relativity, which explained the deviations in the
motions of Mercury without the need to invoke
an unknown intra-Mercurial planet. In May 1929
Erwin Freundlich, Potsdam, photographed the
total solar eclipse in Sumatra, and later carefully
examined the plates which showed a profusion
of star images. Comparison plates were taken
six months later. No unknown object brighter
than 9th magnitude was found near the Sun.
But…
Mercury often played a central role in
arguments against relativity, late into the
twentieth century.
 Many of the earlier proposed solutions are
still being considered from time to time!

Conclusions
The anomalous advance of Mercury’s
perihelion is an interesting historical case.
 For my references, see the written
counterpart to this presentation.
