2.3. (3 pts) Calculate the gravitational acceleration (in m/s2) experienced
by someone on Earth (gEARTH).
2.4. (3 pts) The gravitational acceleration on the Moon (gMOON) is 1.546 m/s2. What
fraction of Earth's
gravitational
acceleration is the Moon's (i.e., calculate gMOON / gEARTH )?
2.5. (1 pt) What physical quantity determines why the Earth's gravitational acceleration is more
than that
on
a moon but less than that on a planet such as Jupiter or Saturn?
2.6. (3 pts) Calculate the approximate escape speed (vESC) for Earth in units of
km / s.
SECTION 3 ACTIVITIES :
3.1. (3 pts) Use Kepler's Third Law to find the orbital period of Pluto in yrs.
[Note: you must use a (in AU)]
3.2. (3 pts) Now use Newton's version of Kepler's Third Law to find the period of
Pluto in years.
[Note: you must use a (in m)]
3.3. (1 pt) Why is there a discrepancy between your answers in #3.1 and #3.2 for Pluto's period?
3.4. (1 pt) Why does this discrepancy exist for Pluto's period even though there is NO
discrepancy if you
do the same calculations for Jupiter?
SECTION 4 ACTIVITIES :
-------------------------------------------------
**EXPERIMENT**
Now we will analyze several different gravity simulations using a computer software program called
Orbit Xplorer v2.0
Under the ‘Start’ menu of your computer, find the planet icon that says 'Orbit Xplorer 2.0' and click on it
to start the software.
The program should begin. If you have a problem, ask your TA for help. Some other
important points:
-If the screensaver comes up at anytime while you’re working, you can restore the program by clicking
on the 'Orbit Xplorer' task bar at the bottom of the computer screen. Do NOT restart the program.
-When the program starts, there will be a menu on the tool bar at the top of the screen labeled 'File'.
Selecting the 'New' option will allow you to create your own simulation, while selecting 'Open' will
guide
you through opening and viewing a pre-made standard simulation.
-This program reads and displays scientific notation in a slightly different manner than we are used to.
To represent 5000, the computer program will write 5.00E3 where E replaces the 'x 10EXPONENT' part.
Here are some examples of how you need to type in numbers when using this program:
350000000 = 3.5 x 108 = 3.5E8
-5 = -5 x 100 = -5E0
0.015 = 1.5 x 10-2 = 1.5E-2
-You can manipulate a simulation’s speed by using the up and down arrows which are located in the
right top corner of each simulation window.
-Do NOT run more than two simulations at the same time.
-Once you open or create a simulation, there will be six menus on the tool bar at the top of the screen.
If you need to know what a menu option is, click on the 'Help' menu and select 'Manual'. Each of
the
other five menus has information listed here. And, if all else fails, ask your TA for help!
--------------------------
SIMULATION A : to compare geocentric and heliocentric models of the Solar System
-Select 'Open' under the toolbar menu called 'File' and open the file “Geocentric and Heliocentric
World View. Sim”.
-Now, open this file a second time. Reduce the size of both windows and place them side by side so you
can view both
of them completely at the same time. If you cannot, just run one at a time.
-In the first Parameters window, find the box labeled 'Position in window'. Make sure it is set with body
#2 (the Earth)
in the center of the window. Do not edit the second Parameters window.
-Click 'OK' in both simulation windows and then select 'Start All' from the 'Simulation' menu on the
toolbar on top of
your screen. Watch both simulations very carefully for several orbits.
A1. (3 pts) Describe the location of planets with respect to the Sun and the shapes of
their orbits in the geocentric model.
A2. (3 pts) Describe the location of planets with respect to the Sun and the shapes of
their orbits in the heliocentric model.
A3. (3 pts) Why does Mars exhibit a strange "looping" behavior in the geocentric model?
You should have noticed the very strange behavior of Mars in the geocentric model simulation. It has
the planet exhibiting
what is known as retrograde motion. If you were to observe and plot the path of Mars
(or any other planet beyond Earth)
across the sky over several months you would see it make these "loops".
This occurs because Mars is farther from the
center of the Solar System than Earth, and so it travels slower.
This creates a lag and causes our viewpoint to overtake
Mars making Mars appear to move in a strange way.
This observation did not match up with the long-standing geocentric
theory of the planets orbiting Earth in
perfect circles. This was one of the main observations which prompted astronomers
to eventually come to
the correct conclusion that our Solar System is in fact actually heliocentric (Sun-centered).
--------------------------
SIMULATION B : to study the gravitational acceleration on a planet
-Select 'Open' under the toolbar menu called 'File' and open the file named “Rocket Launch. Sim”.
-Click 'OK' in the Parameters window. Start the simulation. You will need to press the arrow buttons
in the upper
righthand corner to slow down the simulation speed.
B1. (2 pts) Watch the rocket travel away from Earth. Stop the simulation when the
rocket appears to temporarily stop
above the Earth. Below, record the acceleration of the rocket
as a(top). Re-start the simulation and let the rocket crash
back into the surface of Earth. Record this
final acceleration as a(bottom).
a ROCKET (top) = ________________ m/s2
a ROCKET (bottom) = ________________ m/s2
B2. (2 pts) Is the acceleration at Earth’s surface what we should expect?
Why or why not? (Hint: see #2.3)
-Return to the Parameters window. Find the box labeled 'Scale' and set it to 'Automatic'.
Also check the box labeled
'Scaled Size'. In the data table, change the rocket speed (vy) in column 8 of the table to vy =
11200 m/s. (Note: this is
same as 11.2 km/s) Now run the simulation again and watch for at least 165000
seconds. The time is in the white box in
the upper lefthand corner of the simulation window.
B3. (2 pts) Was the rocket finally able to escape Earth’s gravity with this speed? Why?
B4. (2 pts) The space shuttle typically travels a few hundred km above the Earth at a speed of about
7.6 km/s. Is the
space
shuttle still within the gravitational field of Earth? Why?
--------------------------
SIMULATION C : to study fundamental planetary orbital properties
-Select 'New' under the toolbar menu called 'File' to create your own simulation.
-Check that 'No. of Bodies' is set to 2.
-Click on the image of the Sun and drag it to the first box in the 'Name' column of the data table. Click on
the image of
the Earth and drag it to the second box in the 'Name' column. Data for each of these bodies
should appear in the data
table. Check the 'Coordinate System' box and then click 'OK'.
-Before starting the simulation, pull down the 'View' menu on the toolbar at the top of the screen. Check
off both
'Distance' and 'Speed'. Now you can start the simulation by clicking the 'Start' button in the
simulation window.
Watch the simulation for several orbits. Look CAREFULLY at the orbit of the Earth.
C1. (2 pts) Slow down the simulation gradually so that you can stop the Earth at the left-most point in
its orbit directly
on the x-axis. Record the distance and the speed of Earth which is displayed in the
box on the right of the window.
DIST (left) = __________________km
SPEED (left) = __________________m/s
C2. (2 pts) After re-starting the simulation, stop the Earth again when it is at the right-most point in its
orbit directly on
the x-axis. Record the distance and speed here as well.
DIST (right) = __________________km
SPEED (right) = __________________m/s
C3. (2 pts) Based on the distance data above, what is the shape of this orbit? Which of Kepler’s Laws
does this verify?
C4. (2 pts) We know that the planets' orbits are ellipses. In theory, can a planet orbiting a star
have a circular orbit?
Why or why not?
C5. (1 pt) What is a planet's eccentricity if its orbit is a circle?
C6. (2 pts) Examine your answers to questions C1 and C2 above. With respect to the Sun (closer vs. farther),
where
does the planet move fastest? Where does is move slowest?
C7. (1 pt) Which one of Kepler’s Laws does this verify?
C8. (4 pts) Examine this figure and fill in the blanks with the appropriate letters:
aphelion _____
perihelion _____
lowest speed _____
highest speed _____
--------------------------
SIMULATION D: to study a basic characteristic of planetary motion – Kepler’s 3rd Law
-Select 'Open' under the toolbar menu called 'File' and open the file named “Outer Solar System. Sim”.
-Make sure the 'Projection Plane' option is set to 'xy'.
-Click 'OK' in the Parameters window and then run the simulation. Note the white data box in the upper
left-hand
corner of the screen indicating period. You may want to slow the simulation down some.
D1. (2 pts) Carefully compare the orbits of Jupiter and Pluto. Which orbit is larger? Which is less circular?
D2. (1 pt) Which one of Kepler’s Laws is verified by the results of question D1 above?
D3. (2 pts) Stop Jupiter at its leftmost x-axis point and record this period:
PI = _______________
Press start and stop the simulation again after 1 complete orbit. Record the period:
PF = _______________
D4. (3 pts) Use only the year portion of the above results to subtract
(PF - PI) and get the true period P for Jupiter.
D5. (2 pts) The period for Venus is 0.615 yrs. The period for Neptune is 164.8 yrs.
Comparing these to Jupiter's period,
circle the appropriate underlined word to complete these
sentences:
Kepler's Third Law tells us that the farther a planet is from the Sun, the faster / slower
it orbits the Sun.
Given this, there is a direct / inverse relationship between orbital period and semi-major axis.
--------------------------
SIMULATION E: to see that gravity is also important outside the Solar System
-Select 'Open' under the toolbar menu called 'File' and open the file named “Double Star .Sim”.
-Click 'OK'. Start the simulation and watch carefully for about five orbits or so, noting star speeds
and spacing. Stop
the simulation after about 5 orbits or so.
E1. (4 pts) Describe the orbits of the two stars in this binary system. (Use a
drawing to help if you need).
E2. (1 pt) Which body, blue or yellow, had a faster velocity and acceleration?
E3. (3 pts) If we know the period of this system (P = 412800 s) and the semi-major
axis of the smaller star
(a = 1.199 x 1010 m), what is the total stellar mass (M1 + M2) of the system?
E4. (2 pts) Now go to the Parameters window and find the two stellar masses.
Add them together:
Star 1 + Star 2
= _______________________ kg
Was your result for question E3 right?
E5. (3 pts) Remain in the Parameters window. Set the value R(body #2) = 7e5 and run the simulation again.
Observe what happened and give a reason (hint: look at an important equation) to explain why
this is so.
E6. (3 pts) Data shows that approximately 50% of stars in our Galaxy are members of binary systems.
Based on
this simulation’s results, do the orbits of stars obey Kepler’s laws of motion? Why ?
E7. (4 pts) List 4 reasons that illustrate the importance of the force of gravity in the Universe.
* TURN IN THESE ACTIVITIES PAGES TO YOUR TA*
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