Earth-moon system

MOTIONS OF THE EARTH-MOON SYSTEM

Objectives

  • Relate the phases of the moon to its revolution.

  • Describe waxing and waning.

  • Predict how the distance of the moon affects tides.

  • Compare and contrast lunar eclipse with solar eclipse.

Law of Universal Gravitation

  • Definition: Everybody in the universe attracts every other body with a force that is directly proportional to their masses and inversely proportional to the square of the distance between them.

Implications of the Law

  • Gravitational Force:

    • Decreases with distance.

    • The greater the mass, the greater the gravitational pull.

Gravity between the Earth and Moon

  • The Earth and Moon are held together by the force of gravity.

  • Moon Mass: 7.347 imes 10^{22} ext{ kg}

  • Earth Mass: 5.9736 imes 10^{24} ext{ kg}

Relationship of Mass within the Earth-Moon System

  • The significant mass difference means the Moon orbits the Earth due to its gravitational influence.

Characteristics of the Moon

  • The Moon is Earth's only natural satellite.

  • It moves counterclockwise (eastward) when viewed from the Northern Hemisphere.

Moon's Orbit

  • Type of Orbit: Elliptical

    • Perigee: Closest distance to Earth, 362,570 ext{ km}

    • Apogee: Farthest distance from Earth, 405,410 ext{ km}

  • Appearance at Perigee vs. Apogee:

    • At perigee, the Moon looks slightly larger.

    • At apogee, the Moon looks slightly smaller.

Why is the Moon’s Orbit Elliptical?

  • The combination of gravity and the Moon's tendency to remain in straight-line motion results in its elliptical orbit.

  • The Moon moves forward in its orbit constantly while gravity pulls it towards the Earth.

Effects of Earth-Moon System Motion

  • The motions of the Earth-Moon system lead to various phenomena:

    • Phases of the Moon

    • Eclipses of the Moon and the Sun

Moon's Revolution

  • Sidereal Month: The time taken for the Moon to revolve around the Earth is 27 rac{1}{3} ext{ days}.

  • Synodic Month (Lunar Month): The time taken for the Moon to cycle through its phases is 29 rac{1}{2} ext{ days}.

Comparison of the Two Months

  • Sidereal Month: 27.3 ext{ days} (completed revolution relative to distant stars).

  • Synodic Month: 29.5 ext{ days} (measured between successive new moons).

  • The Moon takes an additional 2.2 days to return to the New Moon phase after a complete orbit.

Observing Lunar Phases

  • Observers on Earth see the phases of the Moon as systematic changes in illumination monthly.

Rotation of the Moon

  • Yes, the Moon does rotate.

    • Rotation Period: The period of rotation around its axis is the same as its revolution around the Earth: 27 rac{1}{3} ext{ days}.

    • This synchronous rotation means the same portion of the Moon always faces the Earth.

Phases of the Moon as observed from Earth

  1. New Moon: Entirely dark; lighted half faces away from Earth.

  2. Waxing Crescent: Slender fraction of the day side visible; does not involve Earth's shadow.

  3. First Quarter: At a right angle to the Sun-Earth line; visible from noon to midnight.

  4. Waxing Gibbous: More than half illuminated but less than full.

  5. Full Moon: All of the Moon's day side is visible; occurs when Earth is between the Moon and Sun.

  6. Waning Gibbous: Illumination decreases; rises late at night.

  7. Third Quarter: Half illuminated; rises around midnight, highest at dawn, sets around noon.

  8. Waning Crescent: Seen before dawn; the Moon is near alignment with Earth and Sun again.

Appearance of Moon Phases

  • Starting with New Moon: The lighted half is facing away from Earth.

  • Waxing Phase: As the Moon moves eastward in orbit, it appears farther from the sunset glare, revealing more of its day side.

  • First Quarter: Seen from noon to midnight; the Moon is one-quarter through its 29.5-day cycle.

Eclipses

Types of Eclipses

  • Solar Eclipse: Occurs when the Moon is directly between the Sun and Earth (at New Moon phase).

  • Lunar Eclipse: Occurs when the Moon moves within the Earth's shadow (at Full Moon phase).

Conditions for Eclipses

  • A solar or lunar eclipse does not happen during every New or Full Moon phase due to the alignment and angular relationship of the Earth, Moon, and Sun.

  • Key Condition: An eclipse occurs when the new or full moon coincides with the Moon’s orbit crossing the ecliptic plane.

  • Eclipses typically occur twice a year with a usual frequency of four eclipses and a maximum of seven.

Tides and the Moon

  • The distance and gravitational effect of the Moon play a crucial role in the occurrence and height of tides on Earth.

End of Section

  • Additional inquiries and topics can further explore the intricate relationship and fascinating motions within the Earth-Moon system and beyond.