Jupsat Pro Astronomy Software

Jupiter is one of the brightest objects in the sky, despite its great distance from Earth.The brightness of a celestial object when seen from a given distance is called its apparent magnitude. This scale has no dimensions, but allows comparison between objects. The lower the magnitude number, the brighter the object. The full Moon has magnitude —12.7 and the Sun has —26.7.The faintest stars visible under dark skies are around +6. Jupiter has an apparent magnitude of about —2. Mars is about as bright as Jupiter, and all the other planets are dimmer than the brightest star visible from Earth, which is Sirius, at apparent magnitude —1.46 (Saturn's apparent magnitude is only +0.6).

Jupiter's brightness has made it an enticing target for astronomers for centuries. Galileo discovered the first of its moons, and Giovanni (Jean-Dominique) Cassini, another highly productive Italian astronomer, discovered the planet's bands and the Great Red Spot around 1655 (for more on the amazing Cassini, see the sidebar "Giovanni Cassini" on page 134). Other sources report that Robert Hooke, the great English experimentalist, was the first to see the Great Red Spot, in 1664. In 1664 Cassini made another important observation of Jupiter: It is slightly 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.The flattening cannot be seen easily in the image of Jupiter shown in the upper color insert on page C-1.

Each planet and some other bodies in the solar system (the Sun and certain asteroids) have been given their own symbol as a shorthand in scientific writing. The symbol for Jupiter is shown on page 5.

Fundamental Information about Jupiter ^Along with being the brightest of all planets, Jupiter is by far the most massive. Despite its low density, just higher than that of liquid water on Earth, it is almost four times as massive as its neighbor Saturn, and more than 300 times as massive as the Earth (Saturn's density, strangely, is just more than half of Jupiter's, and is in fact less than the density of water). If Jupiter had been just 15 times more massive nuclear fusion would have begun in its core, and this solar system would have had two stars rather than just one.

Jupiter also excels in its number of known moons (63, about twice as many as Saturn, the next contender) and the largest magnetic field of any planet. Jupiter's huge magnetic field engulfs many of its moons, protecting them from the damages of the solar wind. The table below lists a number of Jupiter's physical characteristics.

Fundamental Facts about Jupiter equatorial radius at the height where atmospheric pressure is one bar polar radius at the height where atmospheric pressure is one bar ellipticity volume average density acceleration of gravity at the equator and at the altitude where atmospheric pressure is one bar magnetic field strength at the surface rings moons

44,424 miles (71,492 km), 11.21 times Earth's radius

41,490 miles (66,770 km)

0.066, meaning the planet's equator is about 6 percent longer than its polar radius 3.42 X 1014 cubic miles (1.43 X 1015 km3), or 1,316 times Earth's volume

4.2 X 1027 pounds (1.9 X 1027 kg), or 317.8 times Earth's mass

83 pounds per cubic foot (1,330 kg/m3) 75.57 feet per second squared (23.12 m/sec2), or 2.36 times Earth's

4.2 X 10-4 tesla, or about 10 times Earth's 3

Jupiter's spin causes its polar flattening and equatorial bulge. 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, as shown in the image here. 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 figure on page 6) is defined as r - r e = ——— r e

The larger radius, the equatorial, is also called the semimajor axis, and the polar radius is called the semiminor axis. Jupiter's semimajor axis is 44,424 miles (71,492 km), and its semiminor axis is 41,490 miles (66,770 km), so its ellipticity (see figure on page 7) is e = 7—2 -66,770 = 0.066

71,492

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 its poles. Being at a different distance from the center of the planet means there is a different amount of mass between the surface and the center of the planet. Mass pulls on

Symbol for Jupiter

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

Ellipticity is the measure of by 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.

nearby objects with gravity (for more information on gravity, see the sidebar "What Makes Gravity?" on page 8). At the equator, where the radius of the planet is larger and the amount of mass beneath is therefore relatively larger, the pull of gravity is actually stronger than it is at the poles. Gravity is therefore 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, and in a gas giant planet, gravity is given as an average at the height where pressure equals one atmosphere.

Just as planets are not truly spheres, the orbits of solar system objects are not circular. Johannes Kepler, the prominent 17th-century German mathematician and astronomer, first realized that the orbits of planets are ellipses after analyzing a series of precise observations of the location of Mars that had been taken by his colleague, the distinguished Danish astronomer Tycho Brahe. Kepler drew rays from the Sun's center to the orbit of Mars, and noted the date and time that

Mars arrived on each of these rays. He noted that Mars swept out equal areas between itself and the Sun in equal times, and that Mars moved much faster when it was near the Sun than when it was farther from the Sun.Together, these observations convinced Kepler that the orbit was shaped as an ellipse, and not as a circle, as had been previously assumed. Kepler defined three laws of orbital motion (listed in the table on page 9), which he published in 1609 and 1619 in his books New Astronomy and The Harmony of theWorld. These three laws are still used as the basis for understanding orbits.

As Kepler observed, all orbits are ellipses, not circles. An ellipse can be thought of simply as a squashed circle, resembling an oval. The proper definition of an ellipse is the set of all points that have the same sum of distances to two given fixed points, called foci.To demonstrate this definition, take two pins, push them into a piece of stiff cardboard, and loop a piece of string around the pins (see figure on page 10).The two pins are the foci of the ellipse. Pull the string away from the pins with a pencil, and draw the ellipse, keeping the string taut around the pins and the pencil all the way around. Adding the distance along the two string segments from the pencil to each of the pins will give the same answer each time: The ellipse is the set of all points that have the same sum of distances from the two foci.

All Planets: Planetary Mass v. Orbital Ellipcidcy

Jupiter j |
J J Uranus | |||

"jEarth Venus | ||||

J Mars | ||||

'Mercury i i |
i i |
i |

0 0.02 0.04 0.06 0.08 Orbital EHipticity

0.12

0 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:

Gm1mn

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 feet (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.

KEPLER'S LAWS | |

Kepler's first law: |
A planet orbits the Sun following the path of an ellipse with the Sun at one focus. |

Kepler's second law: |
A line joining a planet to the Sun sweeps out equal areas in equal times (see figure below). |

Kepler's third law: |
The closer a planet is to the Sun, the greater its speed. This is stated as: The square of the period of a planet T is proportional to the cube of its semimajor axis R, or T a R 2, as long as T is in years and R in AU. |

Sweeping Equal Areas in Equal Times: Kepler's Second Law

Sweeping Equal Areas in Equal Times: Kepler's Second Law

Kepler's second law shows that the varying speed of a planet in its orbit requires that a line between the planet and the Sun sweep out equal areas in equal times.

Making an ellipse with string and two pins: Adding the distance along the two string segments from the pencil to each of the pins will give the same sum at every point around the ellipse. This method creates an ellipse with the pins at its foci.

The mathematical equation for an ellipse is

where x andy are the coordinates of all the points on the ellipse, and a and b are the semimajor and semiminor axes, respectively. The semimajor axis and semiminor axis would both be the radius if the shape was a circle, but two radii are needed for an ellipse. If a and b are equal, then the equation for the ellipse becomes the equation for a circle:

where n is any constant.

When drawing an ellipse with string and pins, it is obvious where the foci are (they are the pins). In the abstract, the foci can be calculated according to the following equations: Coordinates of the first focus

In the case of an orbit, the object being orbited (for example, the Sun) is located at one of the foci (see figure on page 11).

An important characteristic of an ellipse, perhaps the most important for orbital physics, is its eccentricity: a measure of how different the semimajor and semiminor axes of the ellipse are. Eccentricity is dimensionless and ranges from 0 to 1, where an eccentricity of zero means that the figure is a circle, and an eccentricity of 1 means that the ellipse has gone to its other extreme, a parabola (the reason an extreme ellipse becomes a parabola results from its definition as a conic section). One equation for eccentricity is where a and b are the semimajor and semiminor axes, respectively. Another equation for eccentricity is c e = — , a where c is the distance between the center of the ellipse and one focus. The eccentricities of the orbits of the planets vary widely, though most are very close to circles, as shown in the figure on page 12. Pluto has the most eccentric orbit (0.244), and Mercury's orbit is also very eccentric, but the rest have eccentricities below 0.09.

The table on page 13 lists a number of characteristics of Jupiter's orbit. The planet rotates far faster than the Earth, and lies more than

Semimajor and Semiminor Axes, Foci

The semimajor and semiminor axes of an ellipse (or an orbit) are the elements used to calculate its eccentricity, and the body being orbited always lies at one of the foci.

twice as far from the Sun as its inner neighbor Mars. Its orbit is highly regular: Its path is almost circular and tipped very little from the ecliptic plane. Jupiter's rotation axis is similarly almost perfectly perpendicular to its orbital plane, in contrast to planets like the Earth, Mars, and Saturn, which have significant axial tilts (obliquities) that cause these planets to have seasons.

While the characteristics of an ellipse drawn on a sheet of paper can be measured, orbits in space are more difficult to characterize. The ellipse itself has to be described, then the ellipse's position in space, and then the motion of the body as it travels around the ellipse. Six parameters are needed to specify the motion of a body in its orbit and the position of the orbit. These are called the orbital elements (see the figure on page 15).The first three elements are used to determine where a body is in its orbit.

a semimajor axis The semimajor axis is half the width of the widest part of the orbit ellipse. For solar system bodies, the value of the semimajor axis is typically expressed in units of AU. Jupiter's semimajor axis is 5.2044 AU.

e eccentricity Eccentricity measures the amount by which an ellipse differs from a circle, as described above. An orbit with e = 0 is circular, and an orbit with e = 1 stretches into infinity and becomes a parabola. In between, the orbits are ellipses.The orbits of all large planets are almost circles:The Earth, for instance, has an eccentricity of 0.0068, and Jupiter's eccentricity is 0.04839.

Though the orbits of planets are measurably eccentric, they deviate from circularity by very little. This figure shows the eccentricity of Pluto's orbit in comparison with a circle.

Eccentricity of Pluto's Orbit Compared to a Circle

A circle

A circle

JUPITER'S ORBIT | ||

rotation on its axis ("day") |
9.9 Earth hours, but varies from equator to poles, promoting atmospheric mixing | |

rotation speed at equator |
28,122 miles per hour (45,259 km/hour) | |

rotation direction |
prograde (counterclockwise when viewed from above the North Pole) | |

sidereal period ("year") |
11.86 Earth years | |

orbital velocity (average) |
8.123 miles per second (13.07 m/sec) | |

sunlight travel time (average) |
43 minutes and 16 seconds to reach Jupiter | |

average distance from the Sun |
483,696,023 miles (778,412,010 km), or 5.2 AU | |

perihelion |
460,276,100 miles (740,742,600 km), or 4.952 AU from the Sun | |

aphelion |
507,089,500 miles (816,081,400 km), or 5.455 AU from the Sun | |

orbital eccentricity |
0.04839 | |

orbital inclination to the ecliptic |
1.304 degrees | |

obliquity (inclination of equator to orbit) |
3.12 degrees |

M mean anomaly Mean anomaly is an angle that moves in time from 0 to 360 degrees during one revolution, as if the planet were at the end of a hand of a clock and the Sun were at its center. This angle determines where in its orbit a planet is at a given time, and is defined to be 0 degrees at perigee (when the planet is closest to the Sun) and 180 degrees at apogee (when the planet is farthest from the Sun).The equation for mean anomaly M is given as

0 \ t where M is the value of M at time zero, T is the orbital period, and t is the time in question.

The next three Keplerian elements determine where the orbit is in space.

i inclination For the case of a body orbiting the Sun, the inclination is the angle between the plane of the orbit of the body and the plane of the ecliptic (the plane in which the Earth's orbit lies). For the case of a body orbiting the Earth, the inclination is the angle between the plane of the body's orbit and the plane of the Earth's equator, such that an inclination of zero indicates that the body orbits directly over the equator, and an inclination of 90 indicates that the body orbits over the Poles. If there is an orbital inclination greater than zero, then there is a line of intersection between the ecliptic plane and the orbital plane.This line is called the line of nodes. Jupiter's orbital inclination is 1.304 degrees (see table on page 16).

i longitude of the ascending node After inclination is specified, there are still an infinite number of orbital planes possible: The line of nodes could cut through the Sun at any longitude around the Sun. Notice that the line of nodes emerges from the Sun in two places. One is called the ascending node (where the orbiting planet crosses the Sun's equator going from south to north). The other is called the descending node (where the orbiting planet crosses the Sun's equator going from north to south). Only one node needs to be specified, and by convention the ascending node is used. A second point in a planet's orbit is the vernal equinox, the spring day in which day and night have the same length (the word equinox means equal night), occurring where the plane of the planet's equator intersects its orbital plane.The angle between the vernal equinox y and the ascending node N is called the longitude of the ascending node. Jupiter's longitude of the ascending node is 100.45 degrees.

to argument of the perigee The argument of the perigee is the angle (in the body's orbit plane) between the ascending node N and perihelion P measured in the direction of the body's orbit. Jupiter's argument of the perigee is 14.7539 degrees.

The complexity of the six measurements shown on page 15 demonstrates the extreme attention to detail that is necessary when moving from simple theory ("every orbit is an ellipse") to measuring the movements of actual orbiting planets. Because of the gradual changes in orbits over time caused by gravitational interactions of many bodies and by changes within each planet, natural orbits are complex, evolving

Orbital Elements

Orbital Elements

motions.To plan with such accuracy space missions such as the recent A series of parameters called Mars Exploration Rovers, each of which landed perfectly in their orbital elements are used to targets, just kilometers long on the surface of another planet, the describe exactly the orbit of a mission planners must be masters of orbital parameters. body.

Though Jupiter and Saturn have immense gravity fields that tend to pull small bodies like asteroids and comets out of their own orbits and cause them to crash on the giant planets, there are safe, stable orbits near the giant planets for small bodies. Joseph-Louis Lagrange, a famous French mathematician who lived in the late 18th and early 19th centuries, calculated that there are five positions in an orbiting system of two large bodies in which a third small body, or collection of small bodies, can exist without being thrown out of orbit by gravitational forces. More precisely, the Lagrange points mark positions where the gravitational pull of the two large bodies precisely equals the centripetal force required to rotate with them. In the solar system

OBLIQUITY, ORBITAL INCLINATION, AND | |||

ROTATIONAL DIRECTION FOR ALL THE PLANETS | |||

Orbital inclination to the | |||

Obliquity (inclination of |
ecliptic (angle between the | ||

the planet's equator to |
planet's orbital plane and | ||

its orbit; tilt); remarkable |
the Earth's orbital plane); | ||

Planet |
values are in italic |
remarkable values are in italic Rotational direction | |

Mercury |
0° (though some scientists believe the planet is flipped over, so this value may be 180°) |
7.01° |
prograde |

Venus |
7 3 |
3.39° |
retrograde |

Earth |
23.45° |
0° (by definition) |
prograde |

Mars |
25.2° |
1.85° |
prograde |

Jupiter |
3.12° |
1.30° |
prograde |

Saturn |
26.73° |
2.48° |
prograde |

Uranus |
97.6" |
0.77° |
retrograde |

Neptune |
29.56° |
1.77° |
prograde |

Pluto (now classified 122.5° |
17.16° |
retrograde | |

as a dwarf planet) |

the two large bodies are the Sun and a planet, and the smaller body or group of bodies, asteroids. Of the five Lagrange points, three are unstable over long periods, and two are permanently stable. The unstable Lagrange points, L1, L2 and L3, lie along the line connecting the two large masses.The stable Lagrange points, L4 and L5, lie in the orbit of the planet, 60 degrees ahead and 60 degrees behind the planet itself (see figure on page 17).

The asteroids that orbit in the Lagrange points of Jupiter are called Trojan asteroids. Asteroid 624 Hektor orbits 60 degrees ahead of Jupiter, and was the first Trojan asteroid to be discovered, in 1907. Asteroid 624 Hektor is 186 x 93 miles (300 x 150 km), the largest of all the Trojans. There are about 1,200 Trojan asteroids now known. These asteroids are named after the Greek besiegers of Troy in the

Trojan war, and for the Trojan opponents. As these asteroids are discovered, they are named for the men in the battles: Those at the Lagrange point L4 are all meant to be named after Greeks, and those at L5 after Trojans. Unfortunately a few errors have been made, placing people on the wrong side of the battle, and some astronomers affectionately refer to these misnamed asteroids as spies. Asteroid 617 Patroclus, for example, named after a prominent Greek hero, is in the L5 Trojan Lagrange point.

Jupiter orbits the Sun in a highly regular way, with an almost-circular orbit little inclined to the ecliptic, and with its rotation axis almost perpendicular to its orbital plane. Jupiter itself forms a kind of miniature solar system: It has a collection of over 60 moons, from large, volcanically active moons (Io in particular) to a far-flung population of captured asteroids, and even shares its orbit with two populations of Trojan asteroids. This solar system's largest planet and most complex planetary system is almost a miniature solar system in itself.

The Interior of J upi

Having moved past Mars in The Solar System set, we now encounter planets with entirely different appearances and behaviors. Jupiter is the first of the gas giant planets, as different from its inner neighbor Mars as it is possible to be in this solar system.Where Mars is a small rocky planet with an iron-rich metallic core, like Earth, Jupiter is an immense sphere of gaseous, liquid, and metallic hydrogen and helium. Mars has lost its magnetic field, but Jupiter has the most powerful magnetic field in the solar system aside from the Sun's. The interior states and processes of Jupiter and the other gas giants are entirely different from those of the terrestrial planets.

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