Planetary Orbits using Kepler’s Laws 1.1.1c Explain planetary orbits, especially that of the Earth, using Kepler’s laws.

Father of Modern Astronomy Italian scientist Galileo Galilei proved, by discovering four moons orbiting the planet Jupiter, that not all celestial bodies orbit Earth, and therefore, Earth is not necessarily the center of the solar system. Overview of Kepler’s Laws (7 min) We’ll go over them one by one.

Early Ideas Kepler’s First Law From 1576–1601, Danish astronomer Tycho Brahe made accurate observations of planetary positions. Using Brahe’s data, Johannes Kepler demonstrated his first law which states that each planet orbits the Sun in a shape called an ellipse. An ellipse is an oval shape that is centered on two points called the foci instead of a single point, as in a circle.

Early Ideas Kepler’s First Law The major axis, the maximum diameter of the ellipse, is the line that runs through both foci, one of which is always the Sun. Half of the length of the major axis is called the semimajor axis and is equal to the average distance between the Sun and the planet.

Early Ideas Kepler’s First Law An astronomical unit (AU), 1.496 × 108 km, is the average distance between the Sun and Earth. The average distances between the Sun and each planet are measured in astronomical units.

Early Ideas Eccentricity (how “flattened” the circle is) A planet in an elliptical orbit is not at a constant distance from the Sun. Perihelion is when a planet is at the closest point to the Sun in its orbit. Aphelion is when a planet is farthest point from the Sun during its orbit.

Early Ideas Eccentricity Eccentricity, which is the ratio of the distance between the foci to the length of the major axis, defines the shape of a planet’s elliptical orbit. The orbital period is the length of time it takes for a planet or other body to travel a complete elliptical orbit around the Sun.

Early Ideas Kepler’s Second Kepler’s second law states that because a planet moves fastest when close to the Sun and slowest when far from the Sun, equal areas are swept out in equal amount of time. http://www.youtube.com/watch?v=NiWK5z7z_Oc http://www.youtube.com/watch?v=_3OOK8a4l8Y

Early Ideas Kepler’s Third Laws Kepler also found that the square of the orbital period (P) equals the cube of the semimajor axis of the orbital ellipse (a). P 2 = a 3 Planets closer to the sun orbit the sun in less time. Ex. Mercury takes less time to orbit the sun than Saturn. Italian scientist Galileo Galilei proved, by discovering four moons orbiting the planet Jupiter, that not all celestial bodies orbit Earth, and therefore, Earth is not necessarily the center of the solar system. Kepler’s third law states P 2 = a 3, where P is a unit of time measured in Earth years, and a is a unit of length measured in astronomical units.

Overview of Our Solar System Gravity and Orbits Through observations, Newton realized that any two bodies attract each other with a force that depends on their masses and the distance between the two bodies. The force grows stronger in proportion to the product of the two masses, but diminishes as the square of the distance between them increases.

Relative Motion of Earth in Solar System 1.1.1d Explain relative motion of the Earth in the solar system, the solar system in the galaxy, and the galaxy in the universe—including the expanding nature of the universe; Orbital motion (Earth around the Sun- once/year, seasons depend upon an approximate 23.5 degree tilt); Rotation around our axis (day/night)

The Sun-Earth-Moon System The relationships between the Sun, Moon, and Earth are important to us in many ways. The Sun provides light and warmth, and it is the source of most of the energy that fuels our society. The Moon raises tides in our oceans and illuminates our sky with its monthly cycle of phases. Every society from ancient times to the present has based its calendar and its timekeeping system on the apparent motions of the Sun and Moon.

Daily Motions Earth’s Rotation The length of a day as we observe it is a little longer than the time it takes Earth to rotate once on its axis. Our timekeeping system is based on the solar day, which is the time period from one sunrise or sunset to the next. Day/Night clip (30 sec)

Quick questions How many hours are in a day? How many time zones are on Earth?

Why does the Earth spin? http://www.youtube.com/watch?v=TQxeutcYP6I (3 min)

Why does the Earth Spin? The Earth spins because it was made out of dust that was spinning. It continues spinning because mass maintains its state of motion unless acted on by a force. This property is called INERTIA!

The Sun-Earth-Moon System Annual Motions The annual changes in length of days and temperature are the result of Earth’s orbital motion about the Sun. The ecliptic is the plane which Earth orbits about the Sun.

The Sun-Earth-Moon System Annual Motions The Effects of Earth’s Tilt Earth’s axis is tilted relative to the ecliptic at approximately 23.5°. As Earth orbits the Sun, the orientation of Earth’s axis remains fixed in space. At one point, the northern hemisphere of Earth is tilted toward the Sun, while six months later it is tipped away from the Sun. As a result of the tilt of Earth’s axis and Earth’s motion around the Sun, the Sun is at a higher altitude in the sky during summer than in the winter.

Seasons

The Sun-Earth-Moon System Annual Motions The Effects of Earth’s Tilt Altitude is measured in degrees from the observer’s horizon to the object. There are 90 degrees from the horizon to the point directly overhead, called the zenith of the observer.

The Sun-Earth-Moon System Annual Motions Solstices As Earth moves from position 1, through position 2, to position 3, the altitude of the Sun decreases in the northern hemisphere. Once Earth is at position 3, the Sun’s altitude starts to increase as Earth moves through position 4 and back to position 1.

The Sun-Earth-Moon System Annual Motions Solstices The summer solstice occurs around June 21 each year when the Sun is directly overhead at the Tropic of Cancer, which is at 23.5° N. The summer solstice corresponds to the Sun’s maximum altitude in the sky in the northern hemisphere.

Summer Solstice

The Sun-Earth-Moon System Annual Motions The winter solstice occurs around December 21 each year when the Sun is directly overhead at the Tropic of Capricorn which is at 23.5° S. The winter solstice corresponds to the Sun’s lowest altitude in the sky in the northern hemisphere.

The Sun-Earth-Moon System Annual Motions Equinoxes When the Sun is directly overhead at the equator, both hemispheres receive equal amounts of sunlight. The autumnal equinox occurs around September 21, halfway between the summer and the winter solstices when the Sun is directly over the equator.

The Sun-Earth-Moon System Annual Motions Equinoxes The vernal equinox occurs around March 21, halfway between the winter and the summer solstices when the Sun is directly over the equator. For an observer at the Tropic of Cancer or Tropic of Capricorn, the Sun is 23.5° from the point directly overhead during the equinoxes.

Annual Motions The Sun-Earth-Moon System Equinoxes For a person standing at the x at 23.5º N, the Sun would appear in these positions on the winter solstice, the vernal equinox, and the summer solstice. On the autumnal equinox, the Sun would be at the same altitude as on the vernal equinox.

The Sun-Earth-Moon System Phases of the Moon The sequential changes in the appearance of the Moon are called lunar phases. A new moon occurs when the Moon is between Earth and the Sun and we cannot see the Moon because the sunlit side is facing away from us. As the Moon moves along in its orbit, the amount of reflected sunlight that we can see increases until we are able to see the entire sunlit side of the Moon, known as a full moon. Once a full moon is reached, the portion of the sunlit side that we see begins to decrease as the Moon moves back toward the new-moon position.

The Sun-Earth-Moon System Phases of the Moon Synchronous Rotation Synchronous rotation is the state at which orbital and rotational periods are equal. As the Moon orbits Earth, the same side faces Earth at all times because the Moon has a synchronous rotation, spinning exactly once each time it goes around Earth. How does this work? (2 min) https://www.youtube.com/watch?v=UgpIy4tUjFI

The Sun-Earth-Moon System Motions of the Moon The length of time it takes for the Moon to go through a complete cycle of phases is called a lunar month. The length of a lunar month is about 29.5 days, which is longer than the 27.3 days it takes for one revolution, or orbit, around Earth. The Moon also rises and sets 50 minutes later each day because the Moon has moved 13° in its orbit over a 24-hour period, and Earth has to turn an additional 13° for the Moon to rise.