ISP205 Section 2
Lecture#5: Tuesday, January 23

Handouts:

Topics:

  1. Review

    1. 3 Laws of Newton about Force:

      1. No Force, no change in velocity

      2. Force = mass * acceleration, F = M * a

      3. A force acts between 2 objects - for every force there
        is an equal and opposite force.

    2. Newtons Law of Gravity: F = G * M1 M2 / R2     G=6.67x10-11 Nm2/kg2

    3. Astronouts in orbit are weightless because they are in free fall
      If gravity is the same, all objects fall with the same acceleration independent 
      of their mass. (If there is no significant air resistance)
      DEMO: Movie

  2. Angular measurements

    1. Angular separation of 2 objects is angle between the lines connecting the observer
      and both objects (picture)

    2. Angles are measured in degree: 360 degree make circle,
      1 degree has 60' (arc minutes) and 1' has 60'' (arc seconds)

    3. Angular size = Angular separation of the edges of an object

      angular size = true diameter of object / distance * 57.3o

      angular size (and angular separation) are inversely proportional to distance

      very suitable for astronomy as all observers have always (roughly) the same
      distance to stars (celestial sphere concept)

    4. Examples:

      1. Angular size of the moon (as seen from earth): 0.5 degree

      2. Angular size of the sun (as seen from earth): 0.5 degree

      3. Human eye resolves ~8'

      4. Stellar Parallaxe of 61 Cygni: 0.29''

      5. Abberration of starlight on moving earth: 20''

    5. How to measure angular separations/sizes: use your hand at
      armslength ! (see picture)
      (DEMO: measure angular size)

  3. Right Ascension and Declination

    1. Declination (Dec): "latitude" on celestial sphere
      Angle of an object with respect to the celestial equator
      north: positive angles, south: negative angles
      (see picture)

    2. Right Ascension (RA): "longitude" of celestial sphere
      Measured in hours, minutes and seconds, circumference of celestial 
      sphere is 24h, zero is vernal equinox.

      RA increases towards east on celestial sphere.

    3. Example: Betelgeuse has 5h52min RA and 7deg,24min declination
      (see skymap)

    4. RA and Dec form a coordinate system on the celestial sphere that is the
      same for all observers on earth.

      RA and Dec for the stars remain practically constant
      (small changes due to ?)

    5. Declination tells you at which earth latitude a star will be visible (if declination = latitude
      the star moves through your zenith)
      The difference in RA between to stars tells you how long you have to wait to see
      the star with the higher RA at the same meridian.

  4. The seasons

    1. Why are there seasons ? Because the rotation axis of the earth is tilted by 23.5 degree to
      the plane of its orbit around the sun.

    1. The sunlight is more direct in summer. In summer it is therefore more concentrated
      DEMO (see picture)

    2. The sun is in the sky longer in summer 

  5. The length of the day

    1. The solar day: time for the sun to return to the same meridian, 24 h

    2. Siderial day: time or the earth to spin around its axis once, 23h, 56min

    3. Why are they different: because of the motion of the earth around the sun
      (picture)

  6. The length of the year

    1. Tropical year: Time for the earth to orbit the sun once: 365.24 (solar) days.

    2. Therefore: calendars need to be adjusted with leap years.

  7. The motion of the moon

    1. The moon orbits the earth in 29.5 days

    2. The phases of the moon: (figure from book)

  8. Tides

    1. The gravity of the moon is not the same everywhere on earth - the earths oceans
      become deformed (like a football) (picture from book)

    2. There are 2 tide bulges: on towards the moon and one away from the moon.
      (a football has 2 ends). Therefore time between high tides 12h.

  1. Eclipses

    1. Solar eclipse: Sun and moon have roughly the same angular size, therefore
      the moon can sometimes cover the sun. The earth is then in the shadow of the moon (picture)
      Phase of the moon ?

    2. The orbit of the moon is inclined by 5 degree to the ecliptic. There is not an eclipse every month.

    3. Lunar eclipse: The moon is in the shadow of the earth. (same picture)
      Phase of the moon ?