# Proffessor: J. C. Cersosimo

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1 Proffessor: J. C. Cersosimo

2 Objectives Student will: Recognize the Solar and Lunar calendar Demonstrate the how the Moon phases form Explain the main elements of an orbits Describe the orbit of the Earth Explain how the Seasons happen Demonstrate how occur the Eclipses of Sun and Moon Identify Planets and stars Compute sidereal and synodic periods of planets and moons

3 Calendars In the beginning of astronomy the first calendars showing seasonal changes were based on Moon changes. Calendars were developed by Mayas, Aztecans, Chinese, Babylonians, Egyptians, and may be much more. Incisiones sobre hueso de águila. Meanwhile the sun is a bright disc and on of the heaven, the moon strike the observer and once seen to take place in a regular order and at about the same intervals of time. Phases of the moon would naturally suggest itself as a convenient measure of time; such as day, month and year. The ecliptic is the path of the sun, this is a great circle having its centre at the centre of the sphere. The Chinese claim to have measured the obliquity in 1100 B.C. ( ' ). When the Sun crosses the equator the day is equal to the night, and when this occurs the points of the sun s path crossing the equator are called equinoxes; vernal in March and autumnal in September. The time when the Sun is distant from the equator, these points are called solstice, they are called summer solstice, in June and winter solstice in December.

4 Compute of Days One characteristic of early civilized nations was measure the time. There was three independent measurement of time. One of them divided the time from sunrise to sunset and also the night each into 12 equal hours. According to this arrangement the day hour was in summer longer than a night hour and in winter shorter, and the length of an hour varied during the year. The second one unit of time is the lunar month, the period during which the moon goes through her phases; 29.5 days And a third independent unit is the year; days. The origin of the week is quite different from that of the month or year, and rests on certain astrological ideas about the planet. The Greeks, like early nations began with a calendar based on the moon. In the time of Hesiod (750 and 650 BC) a year consisted of 12 months of 30 days. Later Solon ( BC) added to every alternative year a full month. Thus a period of 2 years would contain 13 months of 30 days and 12 of 29 days, or 738 days in all, distributed among 25 months. The average longitude of the year was 369 days and a month of about 29.5 days. A little later, the astronomer Meton about 460 BC discovery the length of 19 years is very nearly equal to 235 lunar months (the difference less than a day). The Meton s Cycle

5 Roman calendar Actually was very confuse; the first calendar was made by firs king of Roma, Romulo. Year 1 of the roman calendar (735 BC). The year was of 304 days and then, about 30 years later, change to 354 days. A satisfactory reform of the calendar was finally effected by Julius Caesar during the short period of his supremacy at Rome, under the advices of an Alexandrine astronomer Sosigenes. In the beginning, to compensate, the Julian calendar had a year of 445 days, then about 45 BC the ordinary year was to be of 365 days, an extra day being added to Febraury every fourth year (our leap year). Egyptian were the first to know the disadvantage of moon calendar compared with the solar calendar. Their fundamental compute of year was ruled by the Nile River. The period of flooding is of 365 days. On the other hand astronomy played a considerable part in religious matters for fixing the dates of festivals and determining the hours of the night. The titles of several temple books are preserved recording the movements and phases of the sun, moon and stars. The rising of Sirius (Egyptian: Sopdet, Greek:Sothis) at the beginning of the inundation was a particularly important point to fix in the yearly calendar.

6 The First Council of Nicaea was a council of Christian bishops convened in Nicaea in Bithynia (presentday İznik in Turkey) by the Roman Emperor Constantine I in AD 325. This first ecumenical council was the first effort to attain consensus in the church through an assembly representing all of Christian world. Its main accomplishments were settlement the calculation of the date of Easter. The date of celebration must be after the sun pass the equinoctial point (between winter and autumn) and the first Sunday after to the first full moon. It was accepted by Anglicans, Asyrians Church of the East, Eastern Orthodox, Oriental Orthodox, Protestants and Roman Catholics. Ptolomey know that the length of the yeas is no exactly , he wrote in the Almagest, a book known in the mean age, teach a year of 365 d 5 hr and 55 min. Then for the time of Roger Bacon was known a year of 365 d 5 hr and 49 min. So the difference is 11 min per year. This imply days per yr or a day in 130 years. The callendar used today was introduced by Pope Gregory XIII, after whom the calendar was named, by a decree signed on 24 February 1582; this is known as The reformed calendar. It was adopted later that year by a handful of countries, with other countries adopting it over the following centuries. The main change was adopt the year 11 minutes shorter than 365 days. Mean tropical year current value The mean tropical year, as of January 1, 2000 was or 365 days, 5 hours, 48 minutes, seconds. This changes slowly; an expression suitable for calculating the length in days for the distant past is T T T 3 where T is in Julian centuries of 36,525 days measured from noon January 1, 2000 TT (in negative numbers for dates in the past). (McCarthy & Seidelmann, 2009, p. 18.; Laskar, 1986)

7 THE MOON

8

9 The phases of the Moon

10 Sideral and Synodic periods of the Moon T P S Earth s period: días Moon s orbital period= 27.3 days, or tropical month Phases s period = 29.5 days S P T

11 Lunar months approximate the mean length of the synodic month of approximately days (29 days, 12 hours, 44 minutes and 3 seconds).but this is only an approximation The sidereal Lunar month is the time for the Moon to return to the same star, days.

12 Anomalistic month The Moon's orbit approximates an ellipse rather than a circle. However, the orientation (as well as the shape) of this orbit is not fixed. In particular, the position of the extreme points (the line of the apsides: perigee and apogee), makes a full circle (lunar precession) in about 18 years. It takes the Moon longer to return to the same apsis because it moved ahead during one revolution. This longer period is called the anomalistic month, and has an average length of days (27 d 13 h 18 min 33.2 s). [Moon s orbital period= 27.3 días, or tropical month] The apparent diameter of the Moon varies with this period, and therefore this type has some relevance for the prediction of eclipses, whose extent, duration, and appearance (whether total or annular) depend on the exact apparent diameter of the Moon. The apparent diameter of the full moon varies with the full moon cycle which is the beat period of the synodic and anomalistic month, and also the period after which the apsides point to the Sun again.

13 THE DAY AND THE YEAR

14 Mean solar and sideral day A. Beguin measure. B. The Earth complete a lap respect to a star. A. The Earth complete a lap respect to the Sun. A solar day is the length of time between two successive passes of the sun across the same spot in the sky (e.g. crossing the meridian, overhead). That time period is, on average, 24:00:00, hours, or one mean solar day. The sidereal day is the time the Earth takes to rotate 360 degrees, that is in relation to the stars. It is 23 hours 56 minutes 4.09 seconds in length when one compares it with mean solar day which is 24 hours in length. [The Earth rotates degrees in 24 hours.] From A to C there are 24 hs. (a tropical day)

15 The seasons Excentricity Variation of the inclination

16 Apparent solar motion

17 It is the tilt of Earth's axial rotation that creates seasons. During the summer (warm) season in the Northern Hemisphere, the North Pole is tilted toward the sun and the sun is high in the sky at noon. This allows the sun's rays to come in more perpendicular to the ground on the Northern Hemisphere. During the winter (cold) season in the Northern Hemisphere, the North Pole is tilted away from the sun. The sun stays close to the horizon, and days are short. In the Southern hemisphere, the sun is high in the sky at noon, and days are longer. This is why the seasons are reverse in the two hemispheres. While those of us living in the Northern Hemisphere enjoy summer, our neighbors in the Southern Hemisphere are experiencing winter

18 Solsticios and equinoccios

19 ECLIPSES

20

21 An anomalistic month is the Moon's orbital period measured from perigee to perigee. An anomalistic month is about days on average. The draconic month or nodal month is the period in which the Moon returns to the same node of its orbit; the nodes are the two points where the Moon's orbit crosses the plane of the Earth's orbit. Its duration is about days on average. Incidentally, the term "Draconic" refers to a mythological dragon, that supposedly lives in the nodes and regularly eats the Sun or Moon at an eclipse

22 Lunar and Solar Eclipses

23 The Saros The Saros cycle is based on the recognition that 223 synodic months approximately equal to 242 draconic months and 239 anomalistic months. However, as this relationship is not perfect, the geometry of two eclipses separated by one Saros cycle will differ slightly. In particular, the place where the Sun and Moon come in conjunction shifts westward by about 0.5 with respect to the Moon's nodes every Saros cycle, and this gives rise to a series of eclipses, called a Saros series, that slowly change in appearance

24 PLANETS

25 Period and frequency of the Planets: Definitions P Orbital Period of the Planet E Orbital Period of the Earth: d. or 1 yr. S Synodic Period (phases seeing from Earth) fp Frequency f P 1 P Let see the application using an example: Let write the revolution of the planets using the frequency that they appear, for example: Mercury need 88 days to complete 1 revolution, that mean P= 88 days. It needs 88 days to complete a revolution. Question: What is the synodic period of Mercury? Kepler did the next: The frequency of Mercury is lesser than the frequency of Earth, so: f f f S P T fs P 88 días fp 88 1 vuelta días

26 Inner Planets The period of inner planets are lesser than of the Earth f f f S P T S P T Example: What is the period of Venur? P 225 días Example: Mercury S 88 d d 1 1 S 116 d f f f S P T S 225 d d 1 1 S 586 d

27 f f f S T P S T P Ejemplo: Marte tiene un período sidereo de 1.88 años S 1 a 1.88 a 1 1 S 2.13 a Outer Planets The period of outer planets are larger than of the Earth Ejemplo: Cuál es el período de Jupiter? Júpiter tiene un período de años f f f S T P S 1 a a 1 1 S 1.09 a

28 2300 ac ac

29 WHAT ARE THE CAUSES OF THE PRECESSION?

30 The precession of the equinoxes refers to the precession of Earth's axis of rotation with respect to inertial space. Hipparchus discovered that the positions of the equinoxes move westward along the ecliptic compared to the fixed stars on the celestial sphere. The exact dates of his life are not known, but astronomical observations attributed to him date from 147 BC to 127 BC and were described in his publications. He is considered the greatest astronomical observer, and perhaps, the greatest overall astronomer of antiquity. Currently, this annual motion is about 50.3 seconds of arc per year or 1 degree every 71.6 years. The process is slow, but cumulative. A complete precession cycle covers a period of approximately 25,765 years, the so called great Platonic year, during which time the equinox regresses over a full 360. Precessional movement also is the determining factor in the length of an Astrological Age.

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