The Earth Fast Facts about a Planet in Orbit

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Humankind has struggled throughout time to understand the shape of the Earth and its movements in the solar system. Understanding that the Earth is a sphere and that it orbits the Sun in a path shaped like an ellipse, governed by the forces of gravity, has been a journey consisting of long periods in which one model of the Earth was widely accepted, interrupted by periods of turmoil when a new idea was tested, argued against, and finally accepted. Space missions have produced some of the most recent confirming information: Few can contest that the Earth is a sphere once they have seen an image of it taken from space.

To a very close approximation, the Earth is a sphere.The sphericity of the Earth has been known and accepted by most peoples and civilizations since at least the second century B.C.E. This is a surprise to many students schooled in the United States, since the curriculum commonly states that Christopher Columbus discovered that the world is round in 1492. Jeffrey Burton Russell and other historians point to the American writer Washington Irving, among others, as the source of the flat-Earth story: Irving made the Columbus story into a tale of Columbus sailing against all advice that his ships would eventually fall off the edge of the Earth, and subsequently finding new continents and demonstrating there was no edge from which to fall. Irving may have had as his source Antoine-Jean Letronne, a French academician, who wrote that medieval Europeans widely believed in a flat Earth, and Irving's reputation was such that his statement was apparently never checked. In fact there have been only a few scholars in each age who believed in a flat Earth, and

Fundamental Information about the Earth

The Moon, Mars, and the Earth fall into a regular size order: Mars's radius is almost exactly twice that of the Moon, and Earth's is almost exactly twice that of Mars. Since the volume of a sphere is related to the cube of its radius (V = 4/3 nr3), the bodies are far more different in terms of volume: Mars has 0.13 times the Earth's volume, and the Moon again 0.13 times Mars's volume. Earth and Mars are shown together in the upper color insert on page C-1 for a size comparison.

Though in many ways Mars resembles the Earth on its surface (deserts, volcanic flows, dry river valleys, ice caps), the small volume and resulting small internal pressures of Mars make its internal processes considerably different from the Earth's. The Earth's density and gravity are larger than Mars's, and Earth has its single large Moon while Mars has two very small moons. These and other physical parameters for the Earth are listed in the table below.

Fundamental Facts about the Earth equatorial radius 3,963.19 miles (6,378.14 km)

polar radius 3,950.01 miles (6,356.75 km)

ellipticity 0.0034, meaning the planet's equator is about one-

third of a percent longer than its polar radius 2.59 X I011 cubic miles (1.08 X I012 km3) 1.32 X I025 pounds (5.9742 X I024 kg) 344 pounds per cubic foot (5,515 kg/m3) 32 feet per square seconds (9.78 m/sec2)

volume mass average density acceleration of gravity on the surface at the equator magnetic field strength at the surface rings moons varies from 2.2 X I0-5 to 6.6 X I0-5 T

their views have not been the most widely held at any time since the Greeks (though there have been a few scholars who believed in a square Earth).The Columbus myth is an example of how easily errors can be repeated and driven into the canon of fact without being checked; no one's word is above verification.

Sailors over two millennia ago noticed that a mountain or another ship seems to rise from the sea as it is approached, and this effect is most easily achieved by sailing on a sphere, and having the other object come above the horizon as it nears.The movement and shapes of shadows as the Sun passes from east to west is another obvious clue. Though the Earth was generally accepted to be spherical, a greater problem was measuring the size of the sphere. One of the earliest known experiments to measure the radius of the Earth was made by Eratosthenes, a Greek mathematician who lived from 276 to 194 b.c.e. in Cyrene, now a part of Libya, and Alexandria, Egypt. Eratosthenes noticed that on the longest day of the year, the summer solstice, a perfectly upright pole casts no shadow. He also noticed that on the same day the bottom of a well is perfectly lit by sunlight: Both these observations mean that the Sun is directly overhead. He realized that if the Earth were round, a pole placed elsewhere would cast a shadow when his pole did not. Eratosthenes placed a pole at Syene, modern-day Aswan, and another about 500 miles (800 km) away, at Alexandria. The lengths of the shadows were measured, and using relatively simple geometry, Eratosthenes was able to measure the circumference of the Earth. His calculation yielded 250,000 stadia, a measure of length used at that time. The length of the Greek stadium is debated and may have been anywhere from 515 to 548 feet (157 to 167 m). Given that unknown, it can still be said that Eratosthenes'

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

measurement was something between a few and less than a half percent in error from the currently accepted value of 24,901 miles (40,075 km) at the equator (see the sidebar "Fundamental Information about the Earth" on page 4).

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 the Earth is shown on page 5.

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 flat-

e i p tening (more commonly called ellipticity, e) is defined as r - r e = ——— r e

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.

All Planets: Planetary Mass v. Orbital Ellipcidcy

Jupiter j

J J Uranus

"jEarth Venus

J Mars

'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.

The larger radius, the equatorial, is also called the semimajor axis, and the polar radius is called the semiminor axis. The Earth's semimajor axis is 3,963.19 miles (6,378.14 km), and its semiminor axis is 3,950.01 miles (6,356.75 km), so its ellipticity (see the figure on page 6) is

3963.19

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.

To a lesser extent, the distance from the surface to the center of the Earth changes according to topography such as mountains or in valleys. 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 Earth. What effect does mass have? Mass pulls with its gravity. At the equator, where the radius of the Earth 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 therefore, is not a perfect constant on any planet: Variations in radius, topography, as well as the density of the material beneath the surface make gravity vary slightly over the surface.This is why planetary gravitational accelerations are generally given as an average value on the planet's equator.

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 m2 are the masses of the two objects that are attracting each other with gravity, and r is the distance between the two objects.

Immediately it is apparent that the larger the masses are, the larger the force of gravity. In addition, the closer together they are (r), 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 feet (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 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.

Gravity on Earth also affects the shape of the top of the ocean. If there is a large mountain at the bottom of the ocean, for example, the surface of the sea is actually depressed by the gravitational attraction of the mountain. Trenches in the ocean floor allow the surface of the ocean to rise up, because there is less mass pulling it down with gravity. The surface of the ocean deviates from horizontal for many reasons. The largest deviations are caused by tides, washing water from one side of the ocean basin to the other. Tides are a long wavelength phenomenon: Their wavelength is approximately the size of the ocean basin.Waves caused by wind have short wavelengths by comparison, and they are highly regular. By examining the average sea level only at small wavelengths while subtracting the effects of wind-driven waves, a picture of the topography of the ocean floor can be made.

Though trenches, mountains, and dense areas in the Earth's crust alter the gravity field on a small scale, the Earth's gravity field also changes on a large scale.The average value of gravity at the surface of the Earth is 32 feet per square seconds (9.8 m/sec2), and variations in its strength are measured in units called galileos (Gal), or in this case, milliGals (0.001 of a galileo). One galileo is about 0.03 feet per square seconds (0.01 m/sec2). Gravity is high over the Philippines, the Andes, and the North Atlantic, and low over Hudson Bay, the Indian Ocean, and the South Atlantic.

Conditions on the surface of the Earth, such as gravity, are controlled in part by the composition and size of the planet, but they are more significantly influenced by how the planet orbits the Sun. Day length, average, high, and low temperatures, the length of the seasons, and the length of the planet's year are all controlled in large part by the rotation of the planet, the tilt of its orbital axis, and the size and shape of its orbit around the Sun.

The length of a day on Earth varies constantly in response to changing interior and atmospheric motion, distance from the Sun, and through gravitational interactions with the Moon and other planets. A commission called the International Earth Rotation and Reference Systems Service was founded in 1987 by the International

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.

Astronomical Union and the International Union of Geodesy and Geophysics to measure and record the rate of Earth's rotation, its celestial orientation, and changes in the Earth's mantle, core, and tides that affect its rotation. The value for day length given in this table, approximately equivalent to 23 hours, 56 minutes, and 4.09 seconds, is an average time for rotation. The time the Earth takes to rotate once on its axis is longest in the winter and shortest in the summer, varying around the average by about a millisecond.

Why, then, is the Earth's sidereal period ("year") listed as 1.0000174 Earth years? Each calendar year measured on Earth is a little bit shorter than the time it takes the Earth to actually orbit the Sun one time. Over four years this extra time adds up to one additional day, and that is the day that makes a leap year.

All orbits are ellipses, not circles. An ellipse can be thought of simply as a squashed circle, resembling an oval. Neptune's orbit is very close to circular, but it is still an ellipse. The proper definition of an ellipse is the set of all points that have the same sum of distances from two given fixed points, called foci. This definition is demonstrated by taking two pins and pushing them into a piece of stiff cardboard, and looping a string around the pins, as shown in the figure below. 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.

The mathematical equation for an ellipse is x2 y2 — + —- = 1, a2 b2

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 were a circle, but two are needed for an ellipse. If a and b are equal, then the equation for the ellipse becomes the equation for a circle:

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

Coordinates of the second focus

In the case of an orbit, the object being orbited (for example, the Sun) is located at one of the foci (see upper figure on page 12).

An important characteristic of an ellipse, perhaps the most important for orbital physics, is its eccentricity: the measure of how different the semimajor and semiminor axes 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

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.

Semimajor and Semiminor Axes, Foci

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 below. Pluto has the most eccentric orbit at 0.244, and Mercury's orbit is also very eccentric, but the rest have eccentricities below 0.09.

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 cirde

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, and then the ellipse's position in space, and then the motion of the body as it travels around the ellipse. The shape of the ellipse and its relation to the Sun help determine the seasons, though the tilt of the planet on its axis is the most important determinant of seasons.

Seasons are created almost exclusively by the tilt of the planet's rotational axis, called its obliquity. While a planet rotates around the Sun, its axis always points in the same direction (the axis does wobble slightly, a movement called precession).The more extreme the obliquity, the more extreme the planet's seasons. The Earth's obliquity is not the most extreme in the solar system, as shown in the table below.

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 7.01°

prograde

believe the planet is flipped

over, so this value may be 180°)

Venus

177.3° 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

122.5° 17.16°

retrograde

Obliquity and the Seasons

Autumnal equinox ca. September 23rd

Winter solstice ca. December 21st

Perihelion January 3

Aphelion 1 July 4

Summer solstice ca. June 21st

24-hour sun

Sun overhead

No sun

Autumnal equinox ca. September 23rd

Winter solstice ca. December 21st

Perihelion January 3

Aphelion 1 July 4

Summer solstice ca. June 21st

24-hour sun

Sun overhead

No sun

Northern Hemisphere Summer

No sun

24-hour sun

Northern Hemisphere Summer

No sun

24-hour sun

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

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 122.5 degrees. An obliquity above 90 degrees means 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. With the exceptions of Mercury and Jupiter, therefore, all the planets have significant seasons caused by obliquity.

Like its roundness, the Earth's obliquity has been recognized for millennia. In addition to his estimate of the circumference of the Earth, Eratosthenes calculated that the Moon is 780,000 stadia (124,800 km) from the Earth (the currently accepted value is 384,401 km, so in this case his calculation was not very accurate at all). However, Ptolemy records that Eratosthenes also measured the Earth's obliquity as 23.85 degrees, very close to the currently accepted 23.45 degrees.

Obliquity creates seasons by changing the amount of sunlight each hemisphere of the planet experiences from maximum to minimum during each orbit around the Sun (see figure on page 14). When a planet with obliquity has its North Pole tipped toward the Sun, the Northern Hemisphere receives more direct sunlight than does the Southern Hemisphere. The Northern Hemisphere then experiences summer, and the Southern Hemisphere is in winter. The planet progresses in its orbit, revolving around the Sun until it has moved 180 degrees, at which point the Southern Hemisphere gets more direct sunlight, and the Northern Hemisphere is in winter. The more oblique the rotation axis, the more severe the seasons—in summer one hemisphere receives even more sunlight and the other hemisphere even less, and vice versa in winter; summers are hotter and winters are colder. Basic statistics about Earth's orbit are given in the table on page 16.

The obliquity of a planet may change over time as well. Mars's obliquity may oscillate by as much as 20 degrees over time, creating seasons that are much more extreme.The Moon's stabilizing influence on the Earth has prevented large changes in obliquity and helped maintain a more constant climate, allowing life to continue and flourish.

At present the midpoint of summer on Earth for the Northern Hemisphere, when the North Pole points most toward the Sun, is

EARTH'S ORBIT

rotation on its axis ("day")

0.99726968 Earth days

rotation speed at equator

0.29 miles per second (0.47 km/sec)

rotation direction

prograde (counterclockwise when viewed from

above the North Pole)

sidereal period ("year")

1.0000174 Earth years

orbital velocity (average)

18.5 miles per second (29.786 km/sec)

sunlight travel time (average)

8 minutes and 19 seconds to reach Earth

average distance from the Sun

92,958,361 miles (149,597,890 km), or 1 AU

perihelion

91,405,436 miles (147,098,768 km), or 0.9833 AU

from the Sun

aphelion

94,511,989 miles (152,098,144 km) or 1.0167 AU from the Sun

orbital eccentricity

0.01671022

orbital inclination to the ecliptic

0.0 degrees (by definition of the ecliptic)

obliquity (inclination of equator

23.45 degrees

to orbit)

June 21 plus or minus one day, depending on leap years.This is called the summer solstice, the longest day of the year, after which the days gradually become shorter. The Northern Hemisphere's winter solstice, the shortest day of the year, is around December 21.The reverse is true in the Southern Hemisphere: The summer solstice is in December and marks the longest day of the year, and the winter solstice is in June and marks the shortest day of the year.

Along with the summer and winter solstices, there are two other important days, and between these four days, the year is divided into quarters.The vernal equinox is the day in spring on which day and night are the same length (the word equinox means equal night).The autumnal equinox is the day in fall when day and night are the same length.

There are four movements in the Earth's orbit that change the severity of seasons over time. First, the Earth's rotation axis wobbles back and forth along a line of longitude on the Earth, slowly causing a slight change in obliquity.This is called nutation. The Earth's obliquity changes between approximately 22 and 25 degrees on a cycle of about 41,000 years. Nutation is thought to be caused by the Sun and Moon pulling on the Earth's tidal bulge. The Sun's torque on the Earth is at a maximum twice a year, at the solstices, when the Sun is 23.5 degrees above or below the Earth's equatorial plane. Solar torque is at a minimum at the equinoxes, when the Sun is directly above the Earth's equator. Lunar torque, on the other hand, reaches a maximum twice a month.The interaction of these torques causes the Earth's axis to bob in the motion of nutation.

Nutation and Precession

Nutation:

Small-scale circling of the axis creates a nodding motion as the Earth precesses; The motion only takes the axis through 0.20° or less. ^

R = Rotation P = Precession N = Nutation

Precession:

Gradual movement of the Earth's rotational axis around this cone is called precession.

Precession:

Gradual movement of the Earth's rotational axis around this cone is called precession.

R = Rotation P = Precession N = Nutation

Nutation and precession are two movements of the Earth's rotational axis that change the severity of the seasons over time periods of thousands of years.

The direction of tilt of the Earth's axis also changes, much as a toy top does as it is slowing down. This circling of the axis, the second type of movement, is called Chandler wobble after its discoverer, or axial precession. Nutation and precession are shown in the figure on page 17.The cause of precession is not agreed upon, though both the Earth's ellipticity and the sloshing of the oceans due to tides may influence it. A complete circuit of the Earth's axis through precession takes about 25,000 years.

A third effect is called the precession of the equinoxes. Since in summer the Sun shines directly on the hemisphere in question, then the intensity of summer must depend in part on when summer occurs in the planet's orbit. If the planet's axis tilts such that the hemisphere has summer at perihelion, when the planet is closest to the Sun, then it will be a much hotter summer than if that hemisphere had summer at aphelion, when the planet is farthest from the Sun (also, a summer occurring at aphelion will be shorter, since the planet is moving faster). For the Earth, perihelion now occurs in January, making Northern Hemisphere winters slightly milder, and Southern Hemisphere summers slightly hotter. This change in timing of perihelion is known as the precession of the equinoxes, and occurs on a period of 22,000 years (the date of perihelion shifts by about one day in 58 years). Eleven thousand years ago, perihelion occurred in July, making the Northern Hemisphere's winter more severe than it is today.

The fourth effect on the severity of the seasons is a cyclical change in the eccentricity of Earth's orbit. Along with the precession of the equinoxes, the eccentricity of the earth's orbit varies on cycles of 100,000 and 400,000 years, affecting how important the timing of perihelion is to the strength of the seasons: A more eccentric orbit creates more extreme seasons.

The combination of the 41,000-year axial nutation cycle and the 25,000-year precession cycles affect the relative severity of summer and winter, and are thought to control the growth and retreat of ice sheets.The climate cycle caused by the combination of these effects is called the Milankovitch cycle. Cool summers in the Northern Hemisphere, where most of the Earth's landmass is located, appear to allow snow and ice to persist to the next winter, allowing the development of large ice sheets over hundreds to thousands of years. On the other hand, warmer summers shrink ice sheets by melting more ice than the amount accumulated during the winter.

An even more obscure change to the Earth's orbital and rotational cycles is caused by an interaction between the Earth's core and its atmosphere. In ways not entirely understood, the two flowing systems trade energy and can cause changes of day length on the order of two milliseconds per day. This corresponds to a 1 percent change in the average rate of Earth's rotation, and can cause a change in average global wind speed of about 11 miles per hour (18 km/hr).The fact that planetary orbits are ellipses, combined with the fact that the ellipses precess around the Sun slowly, allowed Mars and the Earth to come very close together on August 27, 2003. This close approach was at a distance of 34,776,000 miles (56 million km), not close

Opposition and Conjunction

Opposition and Conjunction

Opposition and conjunction are the two cases when the Earth, the Sun, and the body in question form a line in space.

enough to touch, but closer than the two planets have been in almost sixty thousand years. This kind of close approach is called a perihelic opposition. The orbits had precessed such that their long axes were almost perpendicular to each other. Mars was near perihelion, its closest approach to the Sun, while the Earth was very close to the autumnal equinox, on the side of its ellipse, directly between perihelion and aphelion. Opposition means that the Sun, Earth, and Mars were in a straight line, with Mars directly on the night side of the Earth (see the figure on page 19).The Earth orbits more quickly than Mars, lapping it around the Sun, and every two years the two planets are placed in their orbits in opposition. Normal oppositions occur every two years and bring the planets to within 0.4 to 0.68 AU of each other. Perihelic oppositions only occur about every 15 years, and bring the planets to within 0.37 to 0.4 AU of each other.

The closeness of the planets made Mars appear especially bright to viewers on 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 brightest star is Sirius, with a magnitude of—1.4; the full Moon is —12.7; and the Sun is —26.7. The faintest stars visible under dark skies are around +6. During its close opposition, Mars rose to an apparent magnitude of —2.9, when normally it is as dim as +1.8.

Opposition is an optimal time to launch missions from the Earth to Mars.The spacecraft can be launched before opposition, make an arc between the two planets' orbits at an angle, and then land on Mars just after opposition. On particularly good oppositions the trip between the planets can be made in seven months. Because of the extreme closeness of this opposition, Mars Express and the two Mars Exploration Rover missions to Mars were launched at almost the same time, and all arrived at Mars in January 2004.

As knowledge increases and research continues, the questions scientists pose about the solar system become more complex and focused on more distant bodies. The physics of the sphericity of the Earth, its orbit around the Sun, and the force of gravity are all well understood; their fundamental functioning as described in this chapter are believed to have passed completely into the realm of what is known. Though scientists today might state that these facts and descriptions will stand for all time, perhaps scientists in the past thought the same thing about what they thought to be true. The Catholic Church up to the time of Galileo (the early 17th century) believed completely that the Sun orbited the Earth, and decades and in some cases centuries were required to convince people otherwise. Will modern science be similarly overturned?

With respect to the shape and orbit of the Earth, the answer is certainly no. So many measurements and observations have been taken that the shapes, sizes, and movements of the planets are completely known with such thoroughness that no doubt remains. Some details may still be modified, such as the effects that long-term changes in orbit and obliquity have on climate, but the fundamental physics is known.

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