Handouts:
Topics:
Review
3 Laws of Newton about Force:
No Force, no change in velocity
Force = mass * acceleration, F = M * a
A force acts between 2 objects - for every
force there
is an equal and opposite force.
Newtons Law of Gravity: F = G * M1 M2 / R2 G=6.67x10-11 Nm2/kg2
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
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: measure angular size)
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.
The seasons
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.
The sunlight is more direct in summer. In summer it
is therefore more concentrated
DEMO (see picture)
The sun is in the sky longer in summer
The length of the day
The solar day: time for the sun to return to the same meridian, 24 h
Siderial day: time or the earth to spin around its axis once, 23h, 56min
Why are they different: because of the motion of
the earth around the sun
(picture)
The length of the year
Tropical year: Time for the earth to orbit the sun once: 365.24 (solar) days.
Therefore: calendars need to be adjusted with leap years.
The motion of the moon
The moon orbits the earth in 29.5 days
The phases of the moon: (figure from book)
Tides
The gravity of the moon is not the same everywhere
on earth - the earths oceans
become deformed (like a football) (picture from
book)
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.
Eclipses
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 ?
The orbit of the moon is inclined by 5 degree to the ecliptic. There is not an eclipse every month.
Lunar eclipse: The moon is in the shadow of the
earth. (same picture)
Phase of the moon ?