Course 2: An Introduction to Planet Earth

Radhitya Perdhana, S.Si., M.Sc.

MPG-1101 INTRODUCTORY GEOPHYSICS

GEOPHYSICS STUDY PROGRAM

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The Pale Blue Dot

The Pale Blue Dot is a photograph of Earth taken Feb. 14, 1990, by NASA’s Voyager 1 at a distance of 3.7 billion miles (6 billion kilometers) from the Sun. The image inspired the title of scientist Carl Sagan's book, "Pale Blue Dot: A Vision of the Human Future in Space," in which he wrote: "Look again at that dot.

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The discovery and description of the planets

• Viewed from the wilderness the night sky appear to the naked eye as a canopy of shining points, fixed in space relative to each other
• Early observers noted that the star pattern appeared to move regularly and used this as a basis for determining the timing of events
• The ancient Greeks observed that several celestial bodies moved back and forth against this fixed background and called them the planetes, meaning “wanderers”
• In addition to the Sun and Moon, the naked eye could discern the planets Mercury, Venus, Mars, Jupiter and Saturn
• Geometrical ideas were then introduced into astronomy, which enabled the Greeks to develop astronomy to its highest point in the ancient world
• Aristotle (384–322 BC) summarized the Greek work performed prior to his time and proposed a model of the universe with the Earth at its center (geocentric model)

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• This geocentric model became imbedded in religious conviction and remained in authority until late into the Middle Ages
• It did not go undisputed; Aristarchus of Samos (c.310–c.230 BC) determined the sizes and distances of the Sun and Moon relative to the Earth and proposed a heliocentric (sun-centered) cosmology
• It did not go undisputed; Aristarchus of Samos (c.310–c.230 BC) determined the sizes and distances of the Sun and Moon relative to the Earth and proposed a heliocentric (sun-centered) cosmology
• Ancient astronomers determine the positions and distances of heavenly bodies using the astrolabe

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• In 1543, the year of his death, the Polish astronomer Nicolas Copernicus published a revolutionary work in which he asserted that the Earth was not the center of the universe
• According to his model the Earth rotated about its own axis, and it and the other planets revolved about the Sun
• Copernicus calculated the sidereal period of each planet about the Sun; this is the time required for a planet to make one revolution and return to the same angular position relative to a fixed star
• He also determined the radii of their orbits about the Sun in terms of the Earth–Sun distance
• The mean radius of the Earth’s orbit about the Sun is called an astronomical unit; it equals 149,597,871 km

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Geocentric model

Heliocentric model

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Kepler’s laws of planetary motion

• Kepler took many years to fit the observations of Tycho Brahe into three laws of planetary motion
• the orbit of each planet is an ellipse with the Sun at one focus
• the orbital radius of a planet sweeps out equal areas in equal intervals of time
• the ratio of the square of a planet’s period (T²) to the cube of the semi-major axis of its orbit (a³) is a constant for all the planets, including the Earth
• The nearest and furthest points of a planetary orbit around the Sun are called perihelion and aphelion, respectively
• The terms perigee and apogee refer to the corresponding nearest and furthest points of the orbit of the Moon or a satellite about the Earth

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Characteristics of the planets

• Galileo Galilei (1564–1642) is often regarded as a founder of modern science who made fundamental discoveries in astronomy and physics
• He was one of the first scientists to use the telescope to acquire more detailed information about the planets
• In 1610 Galileo discovered the four largest satellites of Jupiter (called Io, Europa, Ganymede and Callisto), and observed that the planet Venus exhibited different phases of illumination, from full disk to partial crescent 🡺 evidence of Copernian view of the solar system
• In 1781 William Herschel discovered Uranus, the first planet to be found by telescope
• The predicted new planet, Neptune, was discovered in 1846
• In 1914 Percival Lowell predicted the existence of an even more distant planet which culminated in the detection of Pluto in 1930

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• The masses of the planets can be determined by applying Kepler’s third law to the observed orbits of natural and artificial satellites
• Estimation of the sizes and shapes of the planets depends on data from several sources 🡺 early astronomers used occultations of the stars by the planets
• The duration of an occultation depends on the diameter of the planet, its distance from the Earth and its orbital speed
• The dimensions of the planets (Table 1.1) have been determined with improved precision in modern times by the availability of data from spacecraft, especially from radar ranging and Doppler tracking (see Box 1.2)
• The rate of rotation of a planet about its own axis can be determined by observing the motion of features on its surface
• All planets revolve around the Sun in the same sense, which is counterclockwise when viewed from above the plane of the Earth’s orbit (called the ecliptic plane)
• Most of the planets rotate in the same sense as their orbital motion about the Sun, which is termed prograde

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Bode’s law

• In 1772 the German astronomer Johann Bode devised an empirical formula to express the approximate distances of the planets from the Sun
• This series can be expressed mathematically as follows:

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• This expression gives the distance d_n in astronomical units (AU) of the nth planet from the Sun

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Angular momentum

• An important characteristic that constrains models of the origin of the solar system is the difference between the distributions of mass and angular momentum
• For a particle of mass m the moment of inertia (I) about an axis at distance r is defined as

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• The angular momentum (h) is defined as the product of its moment of inertia (I) about an axis and its rate of rotation (Ω) about that axis

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• Each planet revolves in a nearly circular orbit around the Sun and at the same time rotates about its own axis 🡺 there are two contributions to its angular momentum
• The moment of inertia of a planet about the Sun is computed by inserting the mass of the planet and its orbital radius

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• The orbital angular momentum of the planet follows by combining the computed moment of inertia with the rate of orbital revolution
• If the planet is represented by a sphere of mass M and mean radius R, the moment of inertia C about the axis of rotation is given by

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• The angular momentum of a planet’s revolution about the Sun is much greater (on average about 60,000 times) than the angular momentum of its rotation about its own axis
• Whereas more than 99.9% of the total mass of the solar system is concentrated in the Sun, more than 99% of the angular momentum is carried by the orbital motion of the planets, especially the four great planets
• Of these Jupiter is a special case: it accounts for over 70% of the mass and more than 60% of the angular momentum of the planets

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The origin of the solar system

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