JupitersMoons_Worksheet.docx-2
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Clemson University *
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101
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Astronomy
Date
Apr 3, 2024
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4
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Jupiter and its Satellites Worksheet
Student Name: Elizabeth Thompson Section: 007
Observing Jupiter
Table 1
Data
Jupiter
Earth’s Moon
% illumination
99.7%
95.6%
Magnitude
-2.7
-11.9
Rising time
02:07:27 PM
02:53:29 PM
Setting time
05:29:14 AM
05:24:40 AM
Moons of Jupiter
Table 2
Name
Diameter (km)
Orbital Period (days)
Io
3643 km
1.77 days
Europa
3122 km
3.57 days
Ganymede
5262 km
7.16 days
Callisto
4821 km
16.69 days
1)
Were the brightest four moons ever visible all at once to him? If so when?
Jupiter's 4 moon Lo, Europa, Ganymede, Callisto, were all visible to him January 7, 1610.
2)
Do you think the Moon may have made Galileo's observations of Jupiter more difficult?
Why or why not? I think it did because the Earth's moon is larger than Jupiter's moon,
which could have been confusing why trying to figure out which objects are what in the
sky. It also could have potentially blocked the view of some of Jupiter's moons at some
points throughout his observations.
3)
What other planet was close to Jupiter on the night of January 7, 1610?
Uranus.
4)
Center on it. Which direction would Galileo have looked to see it (relative to Jupiter)?
Northeast, at a 45 degree angle from Jupiter.
5)
Center on Mars, then Venus and determine if Galileo could have observed them on
January 7th. Explain your answer.
Mars: No he couldn’t have observed Mars on January 7th 1610 at this time because
Mars was under the horizon.
Venus: No he couldn’t have observed Venus on January 7th 1610 because it was below
the horizon as well.
6)
Observe Jupiter and its moons until 05:00 hours, 5 am.
If Galileo had observed all night, would he have detected the movement of any of the
moons? The movement we are looking for here is their distance from Jupiter.
Name them and describe their movement. Yes he would have observed the movement of
Jupiter's moon throughout the night. The moon is moving somewhat clockwise with the planets
moving further away during their orbital pattern then getting closer again. It appears as if Lo
Europa move across Jupiter. He could’ve been able to detect the movement of the moon until
5am as at 5am they appear to disappear.
Mass of Jupiter
(use the google sheet to help with calculations)
Table 3
Moon
Period (Days)
Period (Years)
Io
1.77 days
0.004849315 years
Europa
3.57 days
0.009780822 years
Ganymede
7.16 days
0.01961644 years
Callisto
16.69 days
0.045726027 years
7)
Distance from Earth to Jupiter (found in info pop up of Jupiter):
4.270480
A.U.
8)
Maximum separation of Jupiter and Ganymede
° ʹ ʺ (as read from measurement tool) = . ° (in decimal degrees only)
On January 7th 0.0846 decimal degrees is the largest distance.
9)
Convert this to radians by dividing by 57.3 degrees/radian:
.00147644 radians.
10) Ganymede’s orbital semi major axis, a = θ (radians) × distance (A.U.) =
0.0063074215 A.U.
11) Since the orbital axis is proportional to the angle, the same scale factor converts one to
the other for all the moons at the same distance from earth.
To find the scale factor divide the moon-Jupiter distance in AU by the moon-Jupiter
separation in decimal degrees.
The Moon to Jupiter distance is 4.27 AU and 0.1825 decimal degrees, which makes the
scale factor 23.397.
Table 4
Moon
Time of
greatest
separation
(hour:min)
Visual Distance
(Decimal
degrees)
Scale factor
Orbital distance
/ semi major
axis (AU)
Io
16:36
0.03777
0.07464
0.002820
Europa
23:59
.09519
0.07511
0.007155
Ganymede
6:03
.06017
0.0745554263
0.004486
Callisto
23:59
0.15844
0.07946
0.01259
Now you can calculate Jupiter’s mass from each moon using Kepler’s Third Law.
M = a
3
/ P
2
You can copy the table created in google sheets here instead of manually typing each number
into this table.
Table 5
Moon
a (A.U.)
P (years)
a
3
P
2
Mass of
Jupiter
(M
sun
)
Io
0.002820
0.004849315
years
2.242576e-8
2.351585e-5
9.53644e-4
Europa
0.007155
0.009780822
years
9.027714e-8
2.012419e-4
4.486e-3
Ganymede
0.004486
0.01961644
years
3.655258e-8
3.848047e-4
9.49899e-4
Callisto
0.01259
0.045726027
years
1.995616e-6
2.090869e-3
9.54443e-4
12) Average of four masses:1.83599e-3 Msun
13) Which moon's value is farthest from the average?
Ganymede is furthest from the average.
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14) Suggest a reason why they do not all give the same answer.
They do not all give the same answer because they are all different distances from Jupiter,
which makes Ganymede being the furthest makes sense.
15) Do a google search to find the mass of Jupiter in terms of the mass of the sun and
compare it to your result. How far off from your calculation is this? Explain how you could
improve your technique to get a more accurate result.
The mass of Jupiter is 1898130 yottagrams which is about 1⁄1000 as massive as the
sun. Our calculations were not far off, we were actually pretty close. Our calculations
were a little overestimated but it was probably due to rounding. This could be prevented
in the future if we were not not round.