Download February 18

Survey of the Universe
Tom Burbine
[email protected]
• HW #2 and Assignment #1 are due Wednesday
Stellar Parallax
• Stellar Parallax – The apparent shift in the
position of a nearby star (relative to distant
objects) that occurs as we view the star from
different positions in the Earth’s orbit of the Sun
each year
The distance the star moves is greatly exaggerated in this figure.
Stellar parallax can only be seen by a telescope.
Ancient astronomers could not detect
stellar parallax
• If Earth orbited the Sun, ancient astronomers
believed that they would see differences in
angular separation of stars as the Earth rotated
around the Sun
• Since they saw no changes in angular separation
of the stars, they assumed the Earth was the center
of the universe
• They could not fathom that stars are so far away
that stellar parallax is undetectable by the human
eye
Nicholas Copernicus (1473-1543)
• Copernicus came up with a model that the Earth
revolves around the Sun (heliocentric model)
• Similar to what Aristarchus (310 – 230 BC)
thought 2,000 years before
• However, Copernicus’ models did not match
observations since he wanted everything to go
around in perfect circles
Tycho Brahe (1546-1601)
• Tycho Brahe was the greatest naked eye observer
of all time
• He lived before the invention of the telescope
• His observations of the alignment of Jupiter and
Saturn occurred two days later than when
predicted by Copernicus
• Tycho came up with a model where the planets
orbit the Sun but the Sun orbits Earth
Johannes Kepler (1571-1630)
• Tried to match circular orbits to Tycho’s data
• Couldn’t do it
• Because Tycho’s observations were so good,
Kepler had to come up with a new model
Kepler was trying to match an orbit to
Tycho’s observations of Mars
• “If I believed that we could ignore these eight
minutes of arc, I would have patched up my
hypothesis accordingly. But, since it was not
permissible to ignore, those 8 minutes pointed to
the road to a complete reformation in astronomy.”
• Kepler came up with his 3 laws of planetary
motion
Kepler’s
st
1
Law
• The orbit of each planet about the Sun is an
ellipse with the Sun at one focus (there is nothing
at the other focus)
Differences between ellipses and circles
Eccentricity (e)
• e = distance between the two foci/length of major axis
• e of circle is 0
• The larger e becomes, the more eccentric the orbit
Definitions
• Perihelion – planet closest to the Sun
• Aphelion – planet farthest from the sun
• Semi-major axis (a) – the average of a planet’s
perihelion and aphelion distances
Kepler’s
nd
2
law
• As a planet moves around its orbit, it sweeps out
equal areas in equal times.
• This means that the planet travels faster when it is
nearer the Sun and slower when it is farther from
the Sun
Kepler’s
rd
3
Law
• More distant planets orbit the Sun at slower
average speeds, obeying the precise mathematical
relationship
p2 = a3
where p is a planet’s orbital period in years and
a is the average distance from the Sun in
astronomical units.
Calculations
• The period for the Earth to go around the Sun is
1 year
• The average distance of the Earth to the Sun is
1 Astronomical Unit
How long does it take Jupiter to go
around the Sun
• If Jupiter is 5.2 Astronomical Units from the Sun,
how long does it take Jupiter to go orbit the Sun
once
• p2 = a3 = 5.23 = 140.6
• p = √140.6 = 11.9 years
Another example
• Mercury is 0.4 Astronomical Units from the Sun.
• How long does it take Mercury to orbit the sun
once?
–
–
–
–
A) 1 year
B) 3 months
C) 9 months
D) 5 years
The calculation
• p2 = a3 = 0.43 = 0.064
• p = √0.064 = 0.25 years
• An asteroid takes 8 years to go around the Sun
• How far is the asteroid away from the Sun?
–
–
–
–
A) 1 AU
B) 3 AU
C) 4 AU
D) 8 AU
The calculation
• a3 = p2 = 82 = 64
• a = (64)1/3 = 4 AU
You can calculate a planet’s orbital speed
• Since you know a planet’s orbital distance
• And you know its orbital time
• You can calculate a planet’s average orbital speed
Orbits
•
all the planets orbit the Sun in a
counterclockwise direction (but they do not orbit
it at the same rate).
•
The Earth rotates counterclockwise
•
The Sun, the Moon, the planets, and the stars all
rise in the east and set in the west
Arguments against the Sun being the
center of the solar system
• 1) If the Earth was moving, objects such as birds
and clouds would be left behind as the Earth
moved
• 2) The heavens must be perfect and unchanging.
Noncircular orbits do not fit this model
• 3) Stellar parallax would be observable
Kepler’s Laws
• http://www.youtube.com/watch?v=dRT3m2Wzyh4
Any Questions?