## Uranus Fast Facts about a Planet in Orbit

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In the 1760s Johann Daniel Titius, a Prussian astronomer at the University of Wittenberg, began thinking about the distances of the planets from the Sun. Why are the inner planets closer together than are the outer planets? In 1766 he calculated the average distance that each planet lies from the Sun, and he noted that each planet is about 1.5 times farther from the Sun than the previous planet. This rule was published and made famous in 1772 (without attribution to Titius) by Johann Elert Bode, a German astronomer and director of the Berlin Observatory, in his popular book Anleitung zur Kenntnis des gestirnten Himmels (Instruction for the knowledge of the starry heavens). Bode did so much to publicize the law, in fact, that it is often known simply as Bode's Law. Both scientists noticed that the rule predicts that a planet should exist between Mars and Jupiter, though no planet was known to be there. There began a significant effort to find this missing planet, leading to the discovery of the main asteroid belt.

Johann Daniel Titius noticed in the mid-18th century that if the planets are numbered beginning with Mercury = 0,Venus = 3, and doubling thereafter, so Earth = 6, Mars = 12, and so on, and four is added to each of the planets' numbers, and then each is divided by 10, a series is created that very closely approximates the planet's distances from the Sun in AU. The final series he came up with is 0.4, 0.7, 1.0, 1.6, 2.8, 5.2, 10. In the table on the next page the planets are listed with their distances from the Sun and the Titius-Bode rule prediction. Remember that these calculations are in astronomical units: Mercury is on average 0.4 AU away from the Sun, and the Earth is 1 AU away.

The original formulation by Titius, published by Bode, stated mathematically, was n + 4

where a is the average distance of the planet from the Sun in AU, and n = 0,3,6, 12,24,48. . . .

Though now the rule is often written, with the same results, as r = 0.4 + 0.3 (2n), where r is the orbital radius of the planet, and n is the number of the planet.

This series actually predicts where Uranus (pronounced "YOOR-un-us") was eventually found, though, sadly, it completely fails for Neptune and Pluto.There is no physical basis for the formation of this rule and there are still no good theories for why the rule works so well for the planets up through Uranus.

About 10 years later, on March 13, 1781, Friedrich Wilhelm Herschel, an amateur astronomer working in Bath, England, first recognized Uranus as a planet (born in Germany in 1738, he was known

TITIUS-BODE RULE PREDICTIONS

 Average AU from Titius-Bode rule Planet/belt the Sun prediction Mercury 0.387 0.4 Venus 0.723 0.7 Earth 1.0 1.0 Mars 1.524 1.6 Asteroid Belt 2.77 2.8 Jupiter 5.203 5.2 Saturn 9.539 10.0 Uranus 19.18 19.6 Neptune 30.06 38.8 Pluto 39.44 77.2

as Frederick William Herschel throughout his adult life in England, and later as Sir Frederick William Herschel). Galileo had seen Uranus in 1548, 233 years earlier, but did not recognize it as a new planet. Uranus is so dim and appears to move so slowly from the Earth's vantage point that it is easily mistaken for a star. In 1690 John Flamsteed, the British Royal Astronomer, also saw Uranus, and also failed to recognize it as a planet. In fact, from the notes of these and other astronomers, it is known that Uranus was seen and described at least 21 times before 1781, but not once recognized as a planet.

Herschel was primarily a musician and composer, though music led him to astronomy (there are intriguing parallels between mathematics, astronomy, and music). In 1773 he bought his first telescope. He and his sister Caroline shared a house in England where they taught music lessons, and soon they were manufacturing telescopes in every moment of their spare time. Around 1770 Herschel decided to "review" the whole sky, that is, to sweep large areas and examine small areas in great detail, to gain "a knowledge of the construction of the heavens." He worked on this immense task for decades. On Tuesday, March 13, 1781, he wrote, "Between ten and eleven in the evening, while I was examining the small stars in the neighborhood of H Geminorum, I perceived one that appeared visibly larger than the rest." This was Uranus. Even Herschel first thought Uranus was a comet, though he wrote that "it appears as a ball instead of a point when magnified by a telescope, and shines steadily instead of twinkling." He wrote a short text called "Account of a Comet," which he submitted to the Royal Society of London.When it was finally determined through continued study of the body by Herschel and others that it was in fact a planet, Herschel's text proved he was its first discoverer.

The recognition of Uranus as a planet doubled the known size of the solar system, and meant that Herschel was the first discoverer of a planet since prehistoric times. Herschel named the planet Georgian Sidus, meaning George's star, after George III, king of England (who had recently had the very great disappointment of losing the American colonies). The planet was called Georgian Sidus in England for almost 70 years despite King George's relative unpopularity. Joseph-Jérôme Lefrançais de Lalande, a French astronomer and mathematician, named the planet Herschel, and in France they called it so for many decades. Other names were suggested, including Cybele, after the mythical wife of the god Saturn. Finally, Johann Elert Bode named the planet Uranus for the Greek and Roman god of the sky who was the father of Saturn,

Many solar system objects have simple symbols; this is the symbol for Uranus.

and that is the name that stuck (it also makes a nice symmetry: In mythology, Uranus is Saturn's father, Saturn is Jupiter's father, and Jupiter is the father of Mercury,Venus, and Mars).

Herschel went on to discover two moons of Uranus and two of Saturn. He died at the age of 84, the exact number of years in Uranus's orbit around the Sun, and so when he died Uranus was in the same place in the sky that it had been when he was born. His sister Caroline, his partner in all his astronomical works, may have been the first female professional astronomer. She made comet-hunting her specialty, and by the time of her death at 98, she had discovered eight new comets.

Each planet and some other bodies in the solar system (the Sun and certain asteroids) have been given its own symbol as a shorthand in scientific writing.The symbol for Uranus is shown in the above figure.

A planet's rotation prevents it from being a perfect sphere. Spinning around an axis creates forces that cause the planet to swell at the equator and flatten slightly at the poles. Planets are thus shapes called oblate spheroids, meaning that they have different equatorial radii and polar radii. If the planet's equatorial radius is called r , and its polar radius is called r , then its flattening (more commonly called ellipticity, e, shown in the figures on pages 8 and 9) is defined as r — r e _ j_^

The larger radius, the equatorial, is also called the semimajor axis, and the polar radius is called the semiminor axis. The Earth's semi-

Fundamental Information about Uranus U ranus is the third of the gas giant planets and shares many characteristics with the other gas planets, most markedly with Neptune. In 1664 Giovanni Cassini, an Italian astronomer, made an important observation of Jupiter: It is flattened at its poles and bulges at its equator. Cassini was exactly right in this observation, and though the effect is extreme on Jupiter, in fact all planets are slightly flattened. Gas planets are particularly susceptible to flattening, and Uranus is no exception, having a radius at its equator about 2 percent longer than its radius at its poles. Its mass is only about 5 percent of Jupiter's, but Uranus is less dense. Uranus thus becomes the third-largest planet, but because of its low density, it is the fourth most massive. These and other physical parameters for Uranus are given in this table.

 Fundamental Facts about Uranus equatorial radius at the height where 15,882 miles (25,559 km), or four times atmospheric pressure is one bar Earth's radius polar radius 15,518 miles (24,973 km) ellipticity 0.0229, meaning the planet's equator is about 2 percent longer than its polar radius volume 1.42 x 1013 cubic miles (5.914 x 1013 km3), or 52 times Earth's volume mass 1.91 x 1026 pounds (8.68 x 1025 kg), or 14.5 times Earth's mass average density 79.4 pounds per cubic foot (1,270 kg/m3), or 0.24 times Earth's density acceleration of gravity on the surface 28.5 feet per squared seconds (8.69 m/sec2), at the equator or 0.89 times Earth's gravity magnetic field strength at the surface 2 x 10-5 tesla, similar to Earth's magnetic field rings 11 moons 27 presently known

major axis is 3,960.8 miles (6,378.14 km), and its semiminor axis is 3,947.5 miles (6,356.75 km), so its ellipticity is

3960.8

Ellipticity is the measure of how much a planet's shape deviates from a sphere.

Ellipticity

In a perfect sphere the polar radius (rp) and equatorial radius (re) are equal.

In this exaggerated example the planet's equatorial radius (re) is longer than its polar radius (rp). This flattening is caused by spin on its axis.

In a perfect sphere the polar radius (rp) and equatorial radius (re) are equal.

In this exaggerated example the planet's equatorial radius (re) is longer than its polar radius (rp). This flattening is caused by spin on its axis.

Because every planet's equatorial radius is longer than its polar radius, the surface of the planet at its equator is farther from the planet's center than the surface of the planet at the poles.What effect does the mass have? Mass pulls with gravity (for more information on gravity, see the sidebar "What Makes Gravity?" on page 10).At the equator, where the radius of the planet is larger and the amount of mass beneath them is relatively larger, the pull of gravity is actually stronger than it is at the poles. Gravity is actually not a perfect constant on any planet:Variations in radius, topography, and the density of the material underneath make the gravity vary slightly over the surface. This is why planetary gravitational accelerations are generally given as an average value on the planet's equator.

Most of the planets orbit in almost exactly the same plane, and most of the planets rotate around axes that lie close to perpendicular to that plane.Though Uranus's orbit lies very close to the solar system's ecliptic plane, its equator lies at almost 98 degrees from its orbital plane. The angle between a planet's equatorial plane and the plane of its orbit is known as its obliquity (obliquity is shown for the Earth on page 11

and given in the table on page 12). The Earth's obliquity, 23.45 degrees, is intermediate in the range of solar system values.The planet with the most extreme obliquity is Venus, with an obliquity of 177.3 degrees, followed by Pluto, with an obliquity of 119.6 degrees. Obliquities above 90 degrees mean that the planet's north pole has passed through its orbital plane and now points south.This is similar to Uranus's state, with a rotational axis tipped until it almost lies flat in its orbital plane.

The only theory that seems to account for Uranus's great obliquity is that early in its accretionary history it was struck by another plan-etesimal, one almost the same size as the proto-Uranus, and the energy of this collision tipped over the rotating planet. Uranus's extreme obliquity, combined with its 84-year orbital period, means that its south and north poles are each in darkness for about 42 years at a time. Uranus's orbit is also anomalous: It is not exactly as it should be as predicted by theory. The differences in its orbit are caused by the gravity of Neptune, and these discrepancies predicted the existence of Neptune and led to its discovery. More measurements of Uranus's orbit are given in the table on page 12. For a complete description of the orbital elements, see chapter 5, "Neptune: Fast Facts about a Planet in Orbit."

There is still an argument, however, over which of Uranus's poles is its north pole. Normally the north pole is easily designated as the

All Planets: Planetary Mass v. Orbital EHipticity

4.5 x 1023 CIO24)

4.5 x 1021 CIO22)

4.5 x 1023 CIO24)

4.5 x 1021 CIO22)

 Jupiter j J J Uranus Venus JMars 'Mercury i i i i i

0.02 0.04 0.06 0.08 Orbital EHipticity

0.12

0.02 0.04 0.06 0.08 Orbital EHipticity

0.12

The ellipticities of the planets differ largely as a function of their composition's ability to flow in response to rotational forces.

What Makes Gravity?

^Gravity is among the least understood forces in nature. It is a fundamental attraction between all matter, but it is also a very weak force: The gravitational attraction of objects smaller than planets and moons is so weak that electrical or magnetic forces can easily oppose it. At the moment about the best that can be done with gravity is to describe its action: How much mass creates how much gravity? The question of what makes gravity itself is unanswered. This is part of the aim of a branch of mathematics and physics called string theory: to explain the relationships among the natural forces and to explain what they are in a fundamental way.

Sir Isaac Newton, the English physicist and mathematician who founded many of today's theories back in the mid-17th century, was the first to develop and record universal rules of gravitation. There is a legend that he was hit on the head by a falling apple while sitting under a tree thinking, and the fall of the apple under the force of Earth's gravity inspired him to think of matter attracting matter.

The most fundamental description of gravity is written in this way:

where F is the force of gravity, G is the universal gravitational constant (equal to 6.67 x 10-11 Nm2/kg2), m and m are the masses of the two objects that are attracting each other with gravity, and r is the distance between the two objects. (N is the abbreviation for newtons, a metric unit of force.)

Immediately, it is apparent that the larger the masses, the larger the force of gravity. In addition, the closer together they are, the stronger the force of gravity, and because r is squared in the denominator, gravity diminishes very quickly as the distance between the objects increases. By substituting numbers for the mass of the Earth (5.9742 x 1024 kg), the mass of the Sun (1.989 x 1030 kg), and the distance between them, the force of gravity between the Earth and Sun is shown to be 8 x 1021 pounds per foot (3.56 x 1022 N). This is the force that keeps the Earth in orbit around the Sun. By comparison, the force of gravity between a piano player and her piano when she sits playing is about 6 x 10-7 pounds per foot (2.67 x 10-6 N). The force of a pencil pressing down in the palm of a hand under the influence of Earth's gravity is about 20,000 times stronger than the gravitational attraction between the player and the piano! So, although the player and the piano are attracted to each other by gravity, their masses are so small that the force is completely unimportant.

Obliquity and the Seasons

Autumnal equinox ca. September 23rd

Winter solstice ca. December 21st

Perihelion January 3

Aphelion July 4

Summer solstice ca. June 21st

24-hour sun

No sun

Autumnal equinox ca. September 23rd

Winter solstice ca. December 21st

Perihelion January 3

Aphelion July 4

Summer solstice ca. June 21st

24-hour sun

No sun

Northern hemisphere Summer

No sun

Northern hemisphere Summer

No sun

A planet's obliquity (the inclination of its equator to its orbital plane) is the primary cause of seasons. This figure describes the obliquity of the Earth.

 URANUS'S ORBIT rotation on its axis ("day") 17 Earth hours, 42 minutes rotation speed at equator 5,788 miles per hour (9,315 km/hour) rotation direction retrograde (clockwise when viewed from above its North Pole); this means it spins backward compared to the Earth sidereal period ("year") 83.74 Earth years orbital velocity (average) 4.24 miles per second (6.83 km/sec) sunlight travel time (average) two hours, 39 minutes, and 31 seconds to reach Uranus average distance from the Sun 1,783,939,400 miles (2,870,972,200 km), or 19.191 AU perihelion 1,699,800,000 miles (2,735,560,000 km), or 18.286 AU from the Sun aphelion 1,868,080,000 miles (3,006,390,000 km), or 20.096 AU from the Sun orbital eccentricity 0.04717 orbital inclination to the ecliptic 0.77 degrees obliquity (inclination of equator to orbit) 97.86 degrees

one that is above the ecliptic, but Uranus's poles lie so close to the ecliptic that it is not clear which should be called the north pole.The magnetic field does not help either, because the orientation of a planet's magnetic field is believed to change over time, as has the Earth's. The direction of the magnetic field is especially unhelpful in the case of Uranus, which has a magnetic field that is not remotely aligned with its poles. If in fact the planet has tipped over slightly less than 90 degrees, rather than slightly more, as described here, then its rotation is direct (in the same sense as the Earth's), rather than retrograde, as listed here.