1ISP 205 - Astronomy Gary D. Westfall Lecture 4

Review of GravityReview 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

€

Force=Gm1m2

R2

2ISP 205 - Astronomy Gary D. Westfall Lecture 4

Measuring AnglesMeasuring 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 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

• Angle = size/distance (for distant objects)

• tan(angle) = size/distance (for close object)

Size

DistanceAngle

3ISP 205 - Astronomy Gary D. Westfall Lecture 4

Measuring AnglesMeasuring 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

4ISP 205 - Astronomy Gary D. Westfall Lecture 4

Units of AnglesUnits 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

5ISP 205 - Astronomy Gary D. Westfall Lecture 4

Locating Places on EarthLocating 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

6ISP 205 - Astronomy Gary D. Westfall Lecture 4

Latitude and LongitudeLatitude 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

7ISP 205 - Astronomy Gary D. Westfall Lecture 4

Locating Places in the SkyLocating 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

8ISP 205 - Astronomy Gary D. Westfall Lecture 4

The SeasonsThe 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

9ISP 205 - Astronomy Gary D. Westfall Lecture 4

The Seasons and SunshineThe 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

10ISP 205 - Astronomy Gary D. Westfall Lecture 4

Sun’s Path in the SkySun’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

11ISP 205 - Astronomy Gary D. Westfall Lecture 4

SolsticesSolstices• On June 22, the northern hemisphere has summer

solstice

• On December 22, the northern hemisphere has winter solstice

12ISP 205 - Astronomy Gary D. Westfall Lecture 4

Keeping TimeKeeping 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

13ISP 205 - Astronomy Gary D. Westfall Lecture 4

Early CalendarsEarly 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

14ISP 205 - Astronomy Gary D. Westfall Lecture 4

Mayan CalendarMayan 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

15ISP 205 - Astronomy Gary D. Westfall Lecture 4

Chinese CalendarChinese 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…

16ISP 205 - Astronomy Gary D. Westfall Lecture 4

Gregorian CalendarGregorian 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