AST 105 Planet Positions Lab Report

Lab Exercise: Planet PositionsThe goal of this lab is to illustrate the scale of the solar system as well as calculate the orbital period of
planets given their positions. The heliocentric longitudes of the planets are plotted in table 1 for the
year 2019. In table 2 you’ll find the average radius of the planet’s orbits. For this lab, we’ll assume
planets’ orbits are relatively circular.
Table 1
UT
Mercury Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
01/01/19 226°
140°
100°
42°
247°
281°
31°
291°
02/01/19 316°
191°
132°
59°
249°
282°
32°
291°
03/01/19 100°
235°
160°
74°
251°
283°
32°
291°
04/01/19 231°
285°
191°
89°
254°
284°
32°
291°
05/01/19 320°
332°
220°
104°
256°
285°
33°
292°
06/01/19 124°
21°
250°
118°
259°
286°
33°
292°
07/01/19 240°
69°
279°
132°
261°
287°
33°
292°
08/01/19 335 °
120°
308°
146°
264°
288°
34°
292°
09/01/19 146°
170°
338°
159°
266°
290°
34°
292°
10/01/19 251°
218°
7°
172°
269°
290°
34°
292°
11/01/19 352°
268°
38°
186°
271°
291°
35°
292°
12/01/19 161°
315°
68°
200°
274°
292°
35°
293°
Table 2
Planet
Orbital Radius (A.U.)
Mercury
0.39
Venus
0.72
Earth
1
Mars
1.52
Jupiter
5.2
Saturn
9.54
Uranus
19.22
Neptune
30.11
On the graph paper, or using a plotting program, create two separate plots. One for the inner planets
(Mercury, Venus, Earth, and Mars) and one for the outer planets (Jupiter, Saturn, Uranus, and Neptune).
The following procedure will cover how to do this using the graphing paper provided. You’ll need a
ruler that has mm marks on it.
1. Measure the width of 10 squares on the graph paper in mm.
Size of 10 squares _________________
The width of the graph paper is 79 squares, the height is approximately 100. On 1 piece of graph paper,
draw 2 suns on the graph paper. Both should be centered on the paper at about 38 or 39 squares from
the left axis. One should be 20 squares from the bottom of the page, the other about 35 squares from the
top. Note that you don’t need to count squares. Since you measured the size of the squares you can
approximate the number using this formula
Measurement (mm)=
Width of 10 Squares (mm)
× number of squares needed
10
Do not draw a line to separate the two graphs. This may cause confusion later on if the graphs
overlap a bit
2. Choose one of the suns to be your inner planet plot. For this plot we’ll be assuming 1 square = 1/10th
of an AU. For mercury, Venus, and earth. Draw in the in the orbits. You can assume the orbits are pretty
much circular. To do this you’ll take the planet’s orbital distance and multiply it by 10 since we are
assuming 1 square=1/10th of an AU. Using Mercury as an example, you’ll draw in an orbit with a
radius of .39 x 10 = 4 squares. Use the equation above to calculate how big 4 squares is on your plot.
You’ll repeat this for Venus and Earth. Since Mars doesn’t make a complete orbit in a year, we’ll need to
modify this. Instead of drawing in a complete orbit for Mars, you’ll calculate the radius of the orbit of
Mars, but only draw the orbit from 42 degrees to 200 degrees.
3. Now repeat the Mars process for the outer planets on the other plot. For the outer planets. Include a
circle showing the size of the earth’s orbit. You do not need to plot the dates of earth’s orbit for this plot.
For this plot, 1 square will equal 1 A.U. Some points may run into the plot for the inner planets. That is
ok.
Questions
For Mercury and Venus, what dates did the planets complete their first full orbit? Note this will be an
approximation.
What is the average angular distance Mercury travels in 1 month (Use the table to calculate this)?
What is the average angular distance Venus travels in 1 month?
If the average month in 2019 is 30.4 days, how many days does it take Mercury and Venus to each
travel around the sun once? To do this use this equation
Number of Days= 360×
30.4 days
degrees travelled during 1 month
How many years is this? (This should be a decimal rounded to the nearest 100th)
For the outer planets, fill in the table below: See below for information on calculating number of Earth
years to complete 1 revolution
Planet
Angular distance Number of Earth Years to Complete 1
Revolution
Mars
Jupiter
Saturn
Uranus
Neptune
To calculate the number of Earth years to complete 1 revolution, use the following formula:
Number of years= 360×
1
Angular distance
1 AU is 93,000 miles. Keeping in mind that the circumference of a circle is C=2πr, complete the
following table. Instructions below will show you how to do this on the next page:
Planet
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Distance From Sun
(miles)
Total distance travelled Distance travelled in 1 Speed in MPH
in orbit (miles)
Earth Day
To calculate the distance from Sun in miles
Distance(miles)= Orbital Radius(A.U.)×
93,000 miles
1 A.U.
To calculate the distance travelled in 1 orbit
Distance travelled = 2 π× Distance from sun (miles)
Distance travelled in 1 earth Day
Distance Travelled =
Total Distance travelled during Orbit
1 year
×
Number of Earth years per orbit
365days
Speed in MPH
Speed (MPH )=
Distance Travelled per Earth Day
24 hours per day
On the second piece of graph paper, create a plot where distance from the sun is the x axis and speed in
MPH is the y axis. Remember the rules to creating a good graph we’ve discussed several times this
semester. Use the whole paper, choose the scales of your axes appropriately, and label the axes. You’ll
want to connect the points you plot but make sure we can still see the plotted points. Graphs that do not
follow these guidelines will receive reduced credit.
Does this graph agree with Kepler’s Laws? Why or why not?
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