Handouts:
Topics:
Review (* = helped to convince people of heliocentric solar system)
Galileo Galilei's discoveries
Milky way consists of individual stars
Landscapes on the moon (*)
Sunspots
Moons of Jupiter (*)
Phases of Venus (*)
Keplers laws (*)
Planets orbit is an ellipse with one focus being the sun
Line connecting sun and planet sweeps over equal areas at equal times
A3=P2 (with A=semimajor axis in AU, P=period in years)
Proof of heliocentric model
Parallax (movement of relative
positions of stars because of the moving
observer)
Aberration of star light (The
angle of light arriving at earth, and therefore
the apparent position of all stars, changes with the observers
motion)
Key concepts of mechanics
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)
Speed
Magnitude of rate of change of position
Example: 60 miles/hour: position changes by 60
miles in an hour
Velocity
Speed and direction of motion
Example 60 miles/hour towards Detroit
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
Force
Outside influence that can change the velocity
of an object by
acting on it (see Newton later ...)
Mass
The amount of matter in an object
Measured on earth using scales (and given in kg
or pounds)
Density
Mass per Volume
Example: 1l water has a mass of 1kg. Density of
water: 1kg/l
or 1g/cm3.
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
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)
Why do Keplers laws work - Newtons theory of mechanics
and gravity
Isaac Newton (1643-1727)
found the
3 Laws that describe classical mechanics:
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)
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)
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
(Mstar+Mplanet)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)
Angular measurements
Angular
separation of 2 objects is angle between the lines connecting the
observer
and both objects (picture)
Angles
are measured in degree: 360 degree make circle,
1 degree has 60' (arc minutes) and 1' has 60'' (arc seconds)
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)
Examples:
Angular size of the moon (as seen from earth): 0.5 degree
Angular size of the sun (as seen from earth): 0.5 degree
Human eye resolves ~8'
Stellar Parallaxe of 61 Cygni: 0.29''
Abberration of starlight on moving earth: 20''
How
to measure angular separations/sizes: use your hand at
armslength ! (see picture)
(Demo: stars on the wall)
How
to locate objects in the sky precisely
Right Ascension and Declination:
Declination
(Dec): "latitude" on celestial sphere
Angle of an object with respect to the celestial equator
north: positive angles, south: negative angles
(see picture)
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.
Example: Betelgeuse has 5h52min RA and 7deg,24min
declination
(see skymap)
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 ?)
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.