An introduction to Astronomy

Moon Phases As the moon revolves around the earth, its position relative to the earth and sun changes. As a result, we on earth view the disk of the moon illuminated by different amounts resulting in what we call phases of the moon. The four main phases of the Moon are New Moon (NM), First Quarter (FQ), Full Moon (FM), and Last Quarter (LQ). Each of these phases of the Moon will occur at the same position relative to the Sun, and therefore each of them rises and sets at the same time each month. The approximate times are as follows: NM– rises around 6am, sets around 6pm FQ – rises around 12pm (noon), sets around 12am (midnight) FM – rises around 6pm, sets around 6am LQ – rises around 12am, sets around 12pm The moon sets approximately 50 minutes later each night. Moon Phase Diagram Fraction of Illumination The fraction of the Moon that we see from Earth is called the fraction of illumination, sometimes noted as a percentage. The fraction of illumination for the phases of the Moon is as follows: There are 7 to 8 days between the new moon and the first quarter, first quarter and full moon, full moon and last quarter, and the last quarter and new moon. On the days in between are crescent and gibbous phases, with the lit potion of the lunar disk getting larger during the “waxing” phases, and smaller during the “waning” phases. The lunar phase cycle is approximately 29.5 days Proceed by doing the exercise for this lab. 9 Language In this laboratory the orbit of the moon will be discussed as well as how to determine if the conditions are right for a solar eclipse or a lunar eclipse to occur. As the Earth orbits the Sun, as seen from the Earth the Sun traces out a path in the sky that is called the Ecliptic. When studying the orbit of the Moon and eclipses it is convenient to define a new coordinate system that is referenced to the plane of the Ecliptic as shown in (figure1). The position of the Sun and Moon in the sky as viewed from Earth is depicted. Ecliptic longitude is measured along the Ecliptic in degrees starting from the position of the Sun on the first day of spring in March. This point is called the First Point of Aries. The Ecliptic longitude of the Sun increases approximately one degree per day as the Sun moves eastward along the Ecliptic. Ecliptic latitude locates an object north or south of the Ecliptic. Eclipses The Moon orbits the Earth in a plane that is inclined to the plane of the Ecliptic at an angle of approximately 5 degrees, as depicted in (figure 1). When the Moon has the same Ecliptic longitude as the Sun it is called a New Moon. When the Moon has an Ecliptic longitude greater than the Sun’s by 180 degrees we call it a Full Moon. It takes approximately 29 ½ days for the Moon to go through all its phases and become a New Moon again. Twice every lunar orbit the Moon crosses the Ecliptic. These two points are known as the Ascending Node and Descending Node. Both the Earth and the Moon cast shadows into space. When the shadow of the Moon falls onto the Earth a Solar Eclipse occurs. When the shadow of the Earth falls onto the Moon a Lunar Eclipse occurs. For a Solar Eclipse to occur, the Moon must cross the Ecliptic within 18.5 degrees of the Sun’s current Ecliptic longitude at New Moon. This region that guarantees an Eclipse is called the Eclipse Limits as shown in (Figure 1). Every six months the Moon crosses the Ecliptic within the Eclipse Limits and an eclipse occurs. An interesting property of eclipses is that nearly identical eclipse occurs every 18 years 11 days and 8 hours. This occurs because the line of nodes rotates in a westward direction taking 18 years to complete a full rotation. In the example discussed later eclipses will occur in Feb and July due to the rotation of the line of nodes. The Moons Orbit When a Satellite orbits the Earth the orbit will be an ellipse (Figure 2). An ellipse has the property that the sum of the distance of the orbiting body from the two foci of the ellipse is a constant. The Earth is located at one foci as shown in figure 2. The point of closest approach is called perigee (Pe), and the point of furthest distance is called apogee (Ap). Eccentricity measures how elongated an orbit is. The higher the eccentricity the more elongated the ellipse. A circle has an eccentricity of zero. The eccentricity can be calculated from the Apogee and Perigee distance of the orbiting body with the following formula;

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