TYPED LETTER SIGNED BY ALBERT EINSTEIN WITH IMPORTANT SCIENTIFIC CONTENT, MAKING HISTORIC CONNECTIONS BETWEEN KEPLER'S WORK AND HIS OWN

EINSTEIN, Albert. Typed letter signed. Princeton, November 3, 1942. One sheet, measuring 8-1/2 by 11 inches, typing on recto only.

An exceptional typed letter signed by Einstein on precursors like Johannes Kepler's work to his Special and General Theories of Relativity,

The letter, on letterhead from the Institute for Advanced Study in Princeton, reads in full: "November 3, 1942. Mr. Felix W. Cartier. Laconite, Minn. Dear Sir: Since the times of Kepler one has found approximation formulaes for the mean distances of the planets from the sun. It is sure that there are not precise laws behind those approximate relations. It may be possible to understand the irregularities of this kind with the methods of statistical mechanics. But hitherto nobody seems to have been able to do so. In any case there is no analogy between such regularities and the quantum laws in molecular physics. Very truly yours, [signed] A. Einstein. Prof. Albert Einstein."

Early in the 17th century, Johannes Kepler (1571-1630) discovered that planets orbit the sun in ellipses rather than perfect circles. This great discovery paved the way for Isaac Newton's laws of gravity, and for Albert Einstein's general and special theories of relativity. Previous to Einstein's time, people believed in real distances and absolute time, and showed that instruments could not objectively measure the distances between planets. Einstein's theories, which hypothesized that light and space curve near a massive object, revolutionized scientific thought and gave man an exciting new perspective of his universe.

Einstein's letter reflects on some of the most important scientific revelations in the history of physics and astronomy. Kepler defined three laws of planetary motion; however, the one specifically referred to in this letter is that all planets move about the Sun in elliptical orbits, having the Sun as one of the foci. If the Universe then consisted only of two point masses—the Sun and a planet—the orbit of that planet would make a perfect, closed ellipse that returned the world to its starting location with each trip around the Sun. But in a Universe governed by Newtonian gravity, with a plethora of massive bodies in our Solar System, that ellipse will precess, or rotate slightly in its orbit.

In the mid-1800s, orbital deviations of Uranus from its predicted motions led to the discovery of Neptune, as the outermost world's gravitational influence accounted for the excess motion. But in the inner Solar System, the nearest planet to the Sun, Mercury, was experiencing a similar problem. With detailed, accurate observations going back to the late 1500s, thanks to astronomer Tycho Brahe, we could measure how Mercury's perihelion, its closest orbital point to the Sun, was advancing. The number we came up with was 5,600" per century, just over 1.5 degrees over a 100 year period. But of that, 5,025" came from the precession of Earth's equinoxes, a well-known phenomenon, while 532" was due to Newtonian gravity.

But 5,025" plus 532" comes up short by a small but significant amount. Attempts at explanation—including the existence of an unknown inner planet, interior to Mercury—all failed. But after Einstein's special theory of relativity came out in 1905, mathematician Henri Poincare showed that the phenomena of length contraction and time dilation contributed a fraction, between 15-25%, of the needed amount towards the solution, dependent on the error. That, plus Minkowski's formalization of space and time as not separate entities, but as a single structure bound together by their union, spacetime, led Einstein to develop the general theory of relativity. On November 25, 1915, he presented his results, computing the spectacular figure that the contribution of the extra curvature of space predicted an additional precession of 43" per century, exactly the right figure needed to explain this observation, sending shockwaves through the astronomy and physics communities. Less than two months after this, Karl Schwarzschild found an exact solution, predicting the existence of black holes. The deflection of starlight and gravitational redshifts/blueshifts were realized as possible tests, and finally the solar eclipse of 1919 validated general relativity as superseding Newtonian gravity.

Expected fold lines. An incredible letter, scarce in its important content.