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Review of Gravity

Learn about gravity's role in planetary orbits, angles, measuring units, and celestial coordinates. Discover how to locate places in the sky and the science behind the changing seasons and sunlight. Explore ancient and modern calendar systems.

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Review of Gravity

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  1. Review of Gravity • The force that hold the planets in orbit is gravity • Gravity is a property of mass • The force of gravity between any two objects is equal to the gravitational constant G times the mass of object 1 times the mass of object 2 divided by the distance between the planet and the sun squared Lecture 4

  2. Measuring Angles Angle • We perceive objects as covering a certain angle • We perceive objects as being separated by a certain angle • Normally angles are giving in degrees • 360 degrees make a complete circle • 2π radians make a circle • By knowing the size of an object and its distance we can calculate the angle Size Distance • Angle = size/distance (for distant objects) • tan(angle) = size/distance (for close object) Lecture 4

  3. Measuring Angles • If you hold your hand out and stretch out your fingers, that is about 20 degrees • If you hold your hand out and make a fist, that is about 10 degrees • If you hold out your hand, your thumb is about 0.5 degree which is about the angular size of the Moon and Sun Lecture 4

  4. Units of Angles • Right ascension • 360 degrees equals 24 hours • 15 degrees of arc equals 1 hour • RA can be given several ways • Vega • 18 h 36.2 m • 18 h 36 m 12 s • 279.05 degrees • Some measurements are given in degrees of arc • 1 degree of arc = 60 minutes of arc • 1 minute of arc = 60 seconds of arc • Arc-degrees • Arc-minutes • Arc-seconds Lecture 4

  5. Locating Places on Earth • Let’s locate our position on the Earth • Use the north and south poles to define a system of coordinates • A great circle is any circle on the surface of the shere whose center is at the center of the sphere • Great circles that pass through the north and south poles are called meridians • Meridians are perpendicular to the equator • Every point on the surface has a meridian passing though it • Longitude • The prime meridian passes through Greenwich, England Lecture 4

  6. Latitude and Longitude • Your latitude is the number of degrees you are away from the equator along your meridian • The North pole is 90 degrees north Lecture 4

  7. Locating Places in the Sky • Positions of objects in the sky are located in a manner similar to latitude and longitude • Declination • Measured on the celestial sphere the same way as latitude with respect to the celestial equator • Polaris is + (north) 90 degrees • Right ascension (RA) • Measured on the celestial sphere the same was as longitude except that the arbitrary zero point is where the ecliptic crosses the celestial equator • There are 360 degrees of RA Lecture 4

  8. The Seasons • We divide the year into 4 season each with different amount of sunlight • The distance from the Earth to the Sun varies only by 3% and we are closer to the Sun when the northern hemisphere has winter • The seasons are caused by the tilt of the Earth’s axis of rotation Lecture 4

  9. The Seasons and Sunshine • In summer, sunlight strikes the Earth more directly, more sunlight per unit area in the northern hemisphere • In winter, the Sun is low in the sky and the sunlight spreads out more per unit area in the northern hemisphere Lecture 4

  10. Sun’s Path in the Sky • In summer, the Sun stays above the horizon for more than 12 hours • Longest day is the summer solstice • In winter, the Sun stays below the horizon for more than 12 hours • Shortest day is the winter solstice • On the vernal and autumnal equinoxes, the day is exactly 12 hours Lecture 4

  11. Solstices • On June 22, the northern hemisphere has summer solstice • On December 22, the northern hemisphere has winter solstice Lecture 4

  12. Keeping Time • A day is the time required for the Earth to rotate once on its axis • The solar day is measured sunrise to sunrise • A sidereal day is measured with respect to the fixed background of stars • A solar day is about 4 minutes longer than a sidereal day • 24 hours/365 • Our normal time is the mean solar day quantized into time zones Lecture 4

  13. Early Calendars • A calendar must keep track of time over a long time and be able to mark events in the past and the future • A calendar must be based on natural time intervals that everyone can agree on • Days • Rotation of the Earth • Months • Orbit of the Moon around the Earth • Years • Orbit of the Earth around the Sun Lecture 4

  14. Mayan Calendar • Mayan calendar • Flourished between 200 and 1000 AD • As sophisticated as contemporary European calendars • Did not correlate with month or year • Recorded the passage of days and forecast events into the future Lecture 4

  15. Chinese Calendar • Developed by court astronomer-astrologers • Took into account • Moon • Earth • 12 year cycle of Jupiter • Current Chinese calendar still incorporates aspects of this 12 year cycle • Year of the dog… Lecture 4

  16. Gregorian Calendar • Modern calendar in use • Update of Julian calendar used by Greeks • In 1582, October 4 was followed by October 15 • England and the American colonies put the Gregorian reform into effect • September 2, 1752 was followed by September 14, 1752 • Russia adopted the Gregorian reforms during the Bolshevik revolution when they dropped 13 days Lecture 4

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