ISP205 Section 2
Lecture#4: Thursday, January 13

Handouts:

Topics:

1. Review (* = helped to convince people of heliocentric solar system)

   1. Galileo Galilei's discoveries

      • Milky way consists of individual stars

      • Landscapes on the moon (*)

      • Sunspots

      • Moons of Jupiter (*)

      • Phases of Venus (*)

   2. Keplers laws (*)

      1. Planets orbit is an ellipse with one focus being the sun

      2. Line connecting sun and planet sweeps over equal areas at equal times

      3. A3=P2 (with A=semimajor axis in AU, P=period in years)

   3. Proof of heliocentric model

      1. Parallax (movement of relative positions of stars because of the moving 
         observer)

      2. Aberration of star light (The angle of light arriving at earth, and therefore
         the apparent position of all stars, changes with the observers motion)
          

2. Key concepts of mechanics

   1. Position

      • Location in space, measured from some starting place
        (for example 2 miles east of here)

      • In a three dimensional world on needs 3 numbers
        (for example: 2 numbers (Right Ascension and Declination) are needed
        to describe the position on the celestial sphere, in addition the distance
        from earth is needed to specify the exact location of the object)
         

   2. Speed

      • Magnitude of rate of change of position

      • Example: 60 miles/hour: position changes by 60 miles in an hour
           

   3. Velocity

      • Speed and direction of motion

      • Example 60 miles/hour towards Detroit
          

   4. Acceleration

      • Rate of change of velocity (has also a magnitude and a direction)

      • Example: Acceleration from gravity on earth's surface is 9.8 m/s²
        towards the center of  the earth
           

   5. Force

      • Outside influence that can change the velocity of an object by 
        acting on it (see Newton later ...)
          

   6. Mass

      • The amount of matter in an object

      • Measured on earth using scales (and given in kg or pounds)
          

   7. Density

      • Mass per Volume

      • Example: 1l water has a mass of 1kg. Density of water: 1kg/l
        or 1g/cm³.
          

   8. Momentum

      • mass * velocity

      • A truck has more momentum than a bicycle (at same speed) 
        and a slow truck has less momentum than a fast truck
        

   9. Angular momentum

      • momentum of an object as it rotates around a fixed point

      • mass * velocity * distance from this fixed point
        (this is a simplification for circular motion)  
        

3. Why do Keplers laws work - Newtons theory of mechanics and gravity
    
   Isaac Newton (1643-1727) found the 3 Laws that describe classical mechanics:
    

   1. If the sum of all the forces on an object is zero, its velocity will not change
       
      For astronomy this means it doesnt take angels to keep things in motion.
      (Demo: frictionless track)
       

   2. Force = mass x acceleration.
       
      Tells you for a given force how much an object accelerates.
      Force is measured in Newton (in mks units).
      heavier objects need more force to reach the same acceleration.
      (Demo: frictionless track)
       

   3. For every force that a body exerts on a second body, there is an equal and opposite force exerted by the second body on the first.
       
      In Astronomy that means if the earth pulls on the moon, the moon pulls on the earth with an equal force !
      (Demo: force meter)
       

   And Newtons found a universal theory of gravity:
      

   • F₁₂ = G * M₁ M₂ / R²     G=6.67x10-11 Nm²/kg²
     attractive force between 2 objects = G times the mass of object 1 time mass of object 2 divided by the distance squared.
     the distance is from center to center of the 2 objects
      

   • Any 2 objects with mass attract each other with such a force
      

   • On earth's surface M₂ = mass of earth, R=earth's radius, 
     F₁₂ = M₁ x 9.8 m/s²
     So an object weighting 80 kg is pulled with a force of 800 N towards earth
      

   • With Newtons law, Keplers third law writes
     (M_star+M_planet)P² = A³   (with any unit system)
      

   • This allows to measure the mass of the sun
      

   • What keeps a planet in orbit ? Gravity between sun and that planet AND momentum
     (Demo)

   What about Keplers second law ?

   • Conservation of angular momentum
     (Demo)
      

4. 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 * 57.3^o
      
      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: stars on the wall)
      

5. How to locate objects in the sky precisely
   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.