Download PTYS/ASTR 206 – Section 2 – Spring 2007 Activity #2: 1/18/07

PTYS/ASTR 206 – Section 2 – Spring 2007
Activity #2: 1/18/07
NAME:____KEY__________________________________________________________
The purpose of this activity is to go over Kepler’s Laws discussed in class and in Chapter 4 of the
textbook. This is an ACTIVITY, so feel free to discuss these with one or two of your neighbors. You
must turn in your own work.
# 1. (4 pts) The orbit of a fictitious planet is shown below. Like all planets that orbit a central star, this
one obeys Kepler’s laws. The twelve positions shown (1-12) are each exactly one month apart.
5
4
6
3
2
1
7
12
11
8
10
9
(a) Does the planet appear to be traveling the same distance each month?
NO
(b) At which position would the planet have been traveling the fastest? The slowest?
How can you tell?
Fastest – 7
Slowest – 1
(c) At position number 4, is the speed of the planet increasing or decreasing as time goes
on? How can you tell?
Increasing because the distance from 3-4 is shorter than from 4-5. Since the distances
between dots are at equal time intervals, a farther distance traveled means it is
moving faster. Thus, its speed is getting larger.
(d) Provide a concise statement that describes the relationship that exists between a
planet’s orbital speed and the distance from its companion star
The speed is larger the closer it is to the star in which it is orbiting.
Continued on the back !
# 2. (3 pts) Consider the table below listing the eccentricity
of the orbit for each planet in the solar system. Recall that
an orbit with an eccentricity of zero is perfectly circular.
(a) Which planets in the solar system would experience
the largest change in orbital speed and which would
experience the smallest change in orbital speed?
Pluto and Mercury -- most eccentric, therefore, the
largest change in orbital speed.
Venus and Nepture – least eccentric, therefore, the
least change in orbital speed.
Planet
Eccentricity of Orbit
Mercury
0.206
Venus
0.007
Earth
0.016
Mars
0.093
Jupiter
0.048
Saturn
0.054
Uranus
0.047
Neptune
0.008
Pluto
0.248
(b) Describe the extent to which that you think Earth’s orbital speed changes throughout
a year? Explain your reasoning.
Earth’s orbital velocity does not vary by much because its orbit is very nearly circular
(very low eccentricity).
(c) Which of the three planet orbits shown below (a, b or c) would you say most closely
matches the shape of Earth’s orbit around the Sun? Explain your reasoning.
a
b
c
a. The Earth’s orbits is very nearly circular
# 3. (3 pts) The NASA mission STEREO, launched last October, is two separate spacecraft
designed to orbit the Sun nearly along a same path as the Earth, with one spacecraft (A) moving
slightly faster that the Earth and the other (B) slightly slower. This will enable stereoscopic images
of the Sun. The two spacecraft separate and will, at some point, be on opposite sides of the Sun.
While both spacecraft, and the Earth, move nearly along the same orbital path around the Sun, in
order for them to move at different speeds, they cannot exactly move along the same path. Which
spacecraft would you expect to be farther away from the Sun and which would you expect to be
closer to the Sun? Explain your reasoning.
Spacecraft A must be slightly closer to the Sun in order to move faster along nearly the same
path as Earth. It will orbit the Sun in slightly under a year.
Spacecraft B must orbit slightly farther away from the Sun than Earth to move slower. It will
orbit the Sun in slightly more than a year.