1. ISP 205 - Astronomy Gary D. Westfall1Lecture 4 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

2. ISP 205 - Astronomy Gary D. Westfall2Lecture 4 Measuring Angles We perceive objects as covering a certain angle We perceive objects as being separated by a certain angle Normally angles are giving in degrees n 360 degrees make a complete circle n 2π radians make a circle By knowing the size of an object and its distance we can calculate the angle Angle = size/distance (for distant objects) tan(angle) = size/distance (for close object) Size Distance Angle

3. ISP 205 - Astronomy Gary D. Westfall3Lecture 4 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

4. ISP 205 - Astronomy Gary D. Westfall4Lecture 4 Units of Angles Right ascension n 360 degrees equals 24 hours u 15 degrees of arc equals 1 hour u RA can be given several ways H Vega H 18 h 36.2 m H 18 h 36 m 12 s H 279.05 degrees Some measurements are given in degrees of arc n 1 degree of arc = 60 minutes of arc n 1 minute of arc = 60 seconds of arc u Arc-degrees u Arc-minutes u Arc-seconds

5. ISP 205 - Astronomy Gary D. Westfall5Lecture 4 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 n Meridians are perpendicular to the equator Every point on the surface has a meridian passing though it n Longitude The prime meridian passes through Greenwich, England

6. ISP 205 - Astronomy Gary D. Westfall6Lecture 4 Latitude and Longitude Your latitude is the number of degrees you are away from the equator along your meridian n The North pole is 90 degrees north

7. ISP 205 - Astronomy Gary D. Westfall7Lecture 4 Locating Places in the Sky Positions of objects in the sky are located in a manner similar to latitude and longitude Declination n Measured on the celestial sphere the same way as latitude with respect to the celestial equator u Polaris is + (north) 90 degrees Right ascension (RA) n Measured on the celestial sphere the same was as longitude except that the arbitrary zero point is where the ecliptic crosses the celestial equator u There are 360 degrees of RA

8. ISP 205 - Astronomy Gary D. Westfall8Lecture 4 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

9. ISP 205 - Astronomy Gary D. Westfall9Lecture 4 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

10. ISP 205 - Astronomy Gary D. Westfall10Lecture 4 Sun’s Path in the Sky In summer, the Sun stays above the horizon for more than 12 hours n Longest day is the summer solstice In winter, the Sun stays below the horizon for more than 12 hours n Shortest day is the winter solstice On the vernal and autumnal equinoxes, the day is exactly 12 hours

11. ISP 205 - Astronomy Gary D. Westfall11Lecture 4 Solstices On June 22, the northern hemisphere has summer solstice On December 22, the northern hemisphere has winter solstice

12. ISP 205 - Astronomy Gary D. Westfall12Lecture 4 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 n 24 hours/365 Our normal time is the mean solar day quantized into time zones

13. ISP 205 - Astronomy Gary D. Westfall13Lecture 4 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 n Days u Rotation of the Earth n Months u Orbit of the Moon around the Earth n Years u Orbit of the Earth around the Sun

14. ISP 205 - Astronomy Gary D. Westfall14Lecture 4 Mayan Calendar Mayan calendar n Flourished between 200 and 1000 AD n As sophisticated as contemporary European calendars n Did not correlate with month or year n Recorded the passage of days and forecast events into the future

15. ISP 205 - Astronomy Gary D. Westfall15Lecture 4 Chinese Calendar Developed by court astronomer-astrologers Took into account n Moon n Earth n 12 year cycle of Jupiter u Current Chinese calendar still incorporates aspects of this 12 year cycle H Year of the dog…

16. ISP 205 - Astronomy Gary D. Westfall16Lecture 4 Gregorian Calendar Modern calendar in use Update of Julian calendar used by Greeks n In 1582, October 4 was followed by October 15 England and the American colonies put the Gregorian reform into effect n September 2, 1752 was followed by September 14, 1752 Russia adopted the Gregorian reforms during the Bolshevik revolution when they dropped 13 days