Astronomy 100
The Solar System
Tuesday, Wednesday, Thursday
Tom Burbine
[email protected]
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 = a 3
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
Laboratory
Any Questions?