Kentucky SkyTalk. A History of Gravity: 300 Years of an Attractive Theory. Tim Knauer University of Kentucky 8 January 2015

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1 Kentucky SkyTalk A History of Gravity: 300 Years of an Attractive Theory Tim Knauer University of Kentucky 8 January 2015

2 Aristotle ( BC) Knew that there were five, and only five, regular solids. Asserted that there were five, and only five, fundamental elements. Earth Air Fire Water Aether

3 Aristotle ( BC) Taught that objects of different mass fell at different rates that were proportional to those masses. i.e. an object that weighed twice as much would fall twice as fast This is easily demonstrated to be false, yet it remained dogma for two millennia.

4 2M Aristotle would have expected the larger mass to fall twice as fast as the smaller mass. M Speed, velocity, and acceleration were ill-defined ideas, and remained so until after the Renaissance.

5 2M M Galileo posed an intriguing problem. Suppose we have two unequal hemispheres. According to Aristotle, the twice-larger mass will fall twice as fast.

6 2M M? Galileo asked: what will happen to the two half-spheres if they are joined by a thread? The thread would weigh almost nothing and its weight could be ignored. What will happen?

2M M? Will the larger mass continue to fall twice as fast as the smaller

Will the smaller mass continue to fall half as fast as the larger mass,

Because the total mass is now 3M, will it fall three times as fast?

7 2M M? Will the larger mass continue to fall twice as fast as the smaller mass and therefore make the smaller mass fall faster? Will the smaller mass continue to fall half as fast as the larger mass, and therefore make the larger mass fall slower? Because the total mass is now 3M, will it fall three times as fast? This kind of argument is called a reductio ad absurdum a result that produces a contradictory result and therefore incorrect.

8 Ansel Adams New Mexico, 1941

9 Isaac Newton Newton started with a simple idea; that all masses attract each other. The force of that attraction is proportional to the product of both masses and inversely proportional to the square of the distance between them. m d =? Force~ mm d 2 M

10 Isaac Newton However, spheres do not occupy single points, but a volume of mass. Each small volume attracted all the other small volumes in the other sphere and vice versa. Newton was really sure that each spherical mass could be reduced to two point masses, but he couldn t prove it.

11 Newton needed a way to simplify the problem on the left to the one shown on the right.

12 So Newton invented The Calculus just to solve this specific problem. His Principia Mathematica revolutionized and cleared up the mess that had been physics to that time. Philosophically, Universal Gravitation presented some troubling questions. What generated the force between masses? How does the Moon know how much the Earth weighs and move accordingly? Yet, it worked magnificently for 200 years. JPL Orbit Animations

Urbain Le Verrier (Mathematician) Johann Galle (Astronomer) John Couch Adams (Mathematician) Le Verrier and Adams independently

1846). Recently available documents give Leverrier the stronger claim.

Galle (Berlin Observatory) had the advantage of an improved set of star charts.

13 Urbain Le Verrier (Mathematician) Johann Galle (Astronomer) John Couch Adams (Mathematician) Le Verrier and Adams independently made predictions of the existence and position of a new planet based on its gravitational perturbations of Uranus (23-24 Sept. 1846). Recently available documents give Leverrier the stronger claim. The astronomers royal in England and France could not be bothered to look for Neptune. Galle (Berlin Observatory) had the advantage of an improved set of star charts. He (and his assistant d Arrest) took less than an hour to find Neptune and were the first humans to look at Neptune and also recognize it as another planet. Earlier observations going back to Galileo were found, but no one previous had recognized Neptune as anything but a star.

14 The Flammarion Book of Astronomy, 1964, p323. Originally published in 1880 by Flammarion and Danjon.

15 Position of Saturn at the time of Neptune s discovery. An annotated section of the chart used to find Neptune, a part of a new star atlas not yet published by the Berlin Academy. This facsimile is displayed as a negative; the original chart plotted black stars on a white background.

After the discovery of Neptune was announced, Adams never claimed priority over LeVerrier and despite international discord between France

16 After the discovery of Neptune was announced, Adams never claimed priority over LeVerrier and despite international discord between France and Britain, they remained collegial. 159 years had passed since the publication of The Principia. Position of Neptune at the time of discovery.

17 Apsidal Precession The orbits of the planets are ellipses and do not trace out exactly the same path each revolution. This is because every planet exerts a gravitational force on every other planet. Mercury s orbit is the most elliptical of the major planets and completes one revolution around the Sun in 88 days. Anomalies would be more easily found in Mercury s orbit.

Apsidal Precession 1 is 1/3600 th of 1 o. Mercury s orbit precesses 543 in 100 years, requiring >250,000 years to complete 1 revolution of the orbital axis.

18 Apsidal Precession 1 is 1/3600 th of 1 o. Mercury s orbit precesses 543 in 100 years, requiring >250,000 years to complete 1 revolution of the orbital axis. Le Verrier could only account for 500 from the perturbation from other planers. To fix this seeming anomaly without changing Universal Gravitation, he proposed a small planet inside the orbit of Mercury.

19 This intra-mercurial planet was named Vulcan after the Roman god of the forge (the LaForge?).

20 INAUGURATION OF THE STATUE OF LEVERRIER. Scientific American ( ); Aug 17, 1889; Vol. LXI., No. 7.; American Periodicals pg. 99

21 THE PLANET VULCAN Scientific American Aug 31, 1878; Vol. XXXIX., No. 9.; American Periodicals pg. 128

22 This eclipse was observed from Flint Island. Total Solar Eclipse Path 3-Jan-1908 History does not record if they made cocoanut telephones to report their findings

XCIX, No. 4 But what to do with the extra 43?

23 SOME RESULTS FROM THE 1908 TOTAL SOLAR ECLIPSE. BY PROF. S. A. MITCHELL, COLUMBIA UNIVERSITY. Scientific American Jul 25, 1908; Vol. XCIX, No. 4 But what to do with the extra 43? Mitchell pioneered solar eclipse photography during 10 solar eclipse expeditions between 1900 and 1937.

Einstein never won a Nobel for Relativity. Relativity was fairly new, but had apparently passed several empirical tests. Einstein was Jewish and the 1920 s saw a resurgence of anti-semitism.

24 Einstein never won a Nobel for Relativity. Relativity was fairly new, but had apparently passed several empirical tests. Einstein was Jewish and the 1920 s saw a resurgence of anti-semitism. His model of gravity eliminated the need for spooky action at a distance, as he referred to Newtonian Gravity. In its stead, he imagined a purely geometrical solution, summarized by John Archibald Wheeler with: Mass tells space how to curve; space tells mass how to move.

Newton s Three Law of Motion

Newton s Three Law of Motion Born in England on Christmas day 1643. Overview Chapter 2b Copernican Revolution Bubonic Plague 1665 While home for 2 years with nothing to do he made his most profound discoveries and proposed his most