Download Motions in the Solar System III

Solar System III - Comets, Titius Bode law, and Observations of Jupiter’s Moons
There is no pre-lab for this lab – just add this work sheet to the Solar System Motions II.
Comets have highly elliptical orbits. From the previous lab,
1. The maximum eccentricity of an ellipse is ________
See this simulation of Haley’s comet and click on the “wide-angle view”. Estimate the ratio of
Rmax (aphelion) to Rmin (perihelion) in this simulation.
2. Rmax : Rmin _____________________
3. Therefore, the eccentricity of the orbit is almost exactly _____________
Now click on the “inner solar system” view.
4. About what orbit do you begin to see Haley’s tail? _________________
5. What is the period of Haley’s comet? ___________________
6. When is its next arrival date? _____________
This simulation, shows a comet and its tail. Answer the following:
7. The comet is fastest
a) never – it’s always the same speed
b) the closer it gets to the sun – Kepler’s 2nd law
c) the farther it is from the sun – Kepler’s 1st law
8. The comet tail gets longest
a) never – it’s always the same length
b) farther from the sun
c) closer to the sun
9. The comet tail is directed
a) always behind it where it just was – like jet exhaust
b) always toward the sun
c) always away from the sun
10. The solar wind (particles from the sun) and light pressure from the sun
a) pull inward to the sun like gravity
b) push outward from the sun
c) go around the sun as it rotates
1
11. From 4-7 we can conclude
a) a comet’s tail propels the comet in its orbit
b) a comet’s tail slows the comet down as it gets toward the sun
c) a comet’s tail is glowing gas and evaporated ice, pushed by the solar wind
The Titius-Bode law
Johann Titius in 1766 and Johann Bode in 1772 discovered that the average distance R of
the planets from the sun closely follows the following law
R = (n + 4)/10
,
n = 0, 3, 6, 12, 24, 48 …
(1)
where R is in AU, and n doubles each time after 0. The modern form is
R = 0.4 + 0.3k
, k = 0, 1, 2, 4, 8, 16, 32, …
(2)
where k is 0 plus a sequence of powers of two. The relationship of k to Pascal’s triangle
is shown in this link. Pascal’s triangle can be used to generate the Fibonacci sequence of
numbers 1,1,2,3,5,8,13,… The Fibonacci sequence is an expression of a growth
phenomenon.
Using (1) and (2) and this link to Fill Table I.
Table I – Titius-Bode formula
Planets
(+minor planets)
Mercury
Venus
Earth
Mars
?
Jupiter
Saturn
Uranus
Neptune
Pluto
R (AU)
n
Titius-Bode (1)
0
3
6
12
24
48
96
192
384
768
1536
k
Eqn. (2)
0
1
2
4
8
16
32
64
128
256
512
12. There seems to be a missing “5th” planet. What dwarf object is found at that R?
dwarf at 5th planet _________________________
13. Neptune and Pluto don’t fit. In what place does Pluto fit instead? _______________
2
Place your drawings of Jupiter (from 9/23 and 9/30) here
14. Jupiter 9/23
15. Jupiter 9/30
16. Name the bright dots near Jupiter shown in your figures (you don’t need to know
which is which).
_____________________________________
17. What name was given to this group of 4 objects (after their famous viewer)
_____________________________________
18. In the 9/23 sketch, what remarkable phenomenon is happening to Jupiter and the
bright spot on its horizon?
_____________________________________
3