f.assignment 2 astr101 (2)
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School
Queens University *
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Course
101
Subject
Astronomy
Date
Apr 3, 2024
Type
Pages
12
Uploaded by LieutenantGoldfish4089
PART I: Astronomy with the Human Eye (The Need for
Telescopes)
Picture of the magazine cover I used as Reference
Picture of the Set-up:
The newspaper is set on the kitchen counter and stands thanks to
a prop behind it. To mark the different distances I used objects with a flat surface, the
side facing the counter is where the maximal distance is delimited. I didn’t have a ruler
or measuring tape so I utilized an online ruler which adapts the centimetric measures to
the screen you’re using
Text to be read
Distance (cm)
Size of Print
Ratio (R)
La Quinzaine
1065
2.7
394.4
littéraire
457
1.2
380.83
Delacroix
320
0.6
533.33
●
‘
representative’ value of R: 436.19
○
394.4 + 380.83 + 533.33 = 1308.56
1308.56 / 3 = 436.1867
Question 1:
●
What size of feature would the astronauts be able to see? 917.03 m
The ISS orbits at an average altitude of 400 kilometers above the Earth. The value of R
is 436.19.
Case 2=Distance/R
Given:
●
Size of Rogers Stadium=200 meters
●
R=436.19
●
Distance D from the ISS to Earth's surface ≈ 400 km (400,000 meters) (NASA(1),
2024.)
●
Minimum Size: 400,000/436.19
●
Given that, would they be able to pick out Rogers Stadium, in Toronto? No
○
The minimum size of details that astronauts could discern on the ground
without aid is approximately 917.03 meters. The Rogers Stadium is about
200 meters across making it smaller than the calculated minimum
discernible size by around 717m. Astronauts would not be able to pick out
the Rogers Stadium with the unaided eye from the ISS
Question 2:
Do you think the Great Wall would be observable from the ISS?
●
Average width of the Great Wall is about 4-5 meters
●
Average height is around 6 to 7 meters (Chinadiscovery)
●
The ISS orbits Earth at an altitude of approximately 400 kilometers
●
Length of the wall is 21,196km (Britannica)
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Using Case 2 from question 1: the minimum size of detail discernible from the ISS is
about 917 meters. And while the Great Wall is indeed extremely long, its width and
length can only be described as narrow from a celestial perspective. The case study’s
minimum size is still much bigger than some of the dimensions of the Great Wall (for
context the Wall’s width would need to be around 204 times as large as it is now to
make up for it). Therefore suggesting that the wall's both width and height are too small
to be discerned from the ISS without any aids.
The idea that the Great Wall is visible from space with the naked eye is more of an
urban legend. The wall's gray-brown color blends in with the natural landscape, and its
relatively narrow width makes it indistinguishable from such a vast distance. Even if it
were to be painted a bright color the distance from the ISS would still make it
challenging to see. Reports from astronauts (including those from China), have
indicated that it's not possible to see the Great Wall from orbit with the unaided eye.
This aligns with the previous calculations.
Source of Chinese astronaut:
https://www.theguardian.com/science/2003/oct/23/thisweekssciencequestions
“Yang told Chinese TV when he returned to Earth last week. "I didn't see the Great
Wall."”
Q
uestion 3:
How big would a feature on the Moon need to be if we are to discern it from the Earth
with the unaided eye? 880.35km
●
Distance from Earth to the Moon: 384,000 km. (NASA(2))
●
R value is 436.19
Minimum size= 384,000*1000(convert to meters)/436.19
= 880350.306059
= 880350.306059/1000
= 880.35 km
●
Lake Ontario stretches around 311 km from Kingston to Hamilton (Sail Lake
Ontario).
○
like we’ve seen with the Great Wall. being long doesn't automatically make
it visible from the ISS. It's more about the size and how it stands out
against the background.
●
For any feature on the Moon to be spotted with just our eyes from Earth it's got to
be at least about 880.35 km big in diameter. Thinking about a big red patch the
size of Lake Ontario, which is roughly 311 km long doesn't quite cut it.
Question 4:
If standing on the Moon, looking at Earth, would you be able to spot Lake Ontario with
just your eyes? No
●
Distance from the Moon to Earth is about 384,000 km.
●
A feature on the Moon needs to be at least approximately 880.35 km wide to be
visible from Earth without aid.
Despite the Earth appearing much larger when observing it from the moon rather than
vice versa, the human eye's ability to resolve details at such distances doesn't
drastically change. With Lake Ontario being about 311 km long it remains well below the
calculated minimum visibility ratio for features observed from the Moon to Earth.
Part II
Table 1
Moon
Date and time of extreme
position
(Zoom is set at 18’:13’)
Measured distance of moon
from the center of Jupiter (cm)
Io
November 15th 2024,
16:46:22
2.9
Europa
November 15th 2024, 17:56
4.8
Ganymede
November 16th 2024,
12:31:00
7.1
Castillo
November 30th 2024, 8:52:57
13.6
Table 2
Moon
Date and time of extreme
position
Distance of the moon from the
centre of Jupiter at that time,
in I.U.
(Distance from center/ Io
distance from center)
Io
November 15th 2024,
16:46:22
1.0
Europa
November 15th 2024, 17:56
1.66
(4.8/2.9)
Ganymede
November 15th 2024,
12:31:00
2.44
(7.1/2.9)
Castillo
November 30th 2024, 8:52:57
4.68
(13.6/2.9)
Table 3
Moon
Start Time
End Time
Orbital Period
in hours
Io
November 15th 2024,
16:46:22
November 17th, 18:35:00
49.63
Europa
November 16th 2024,
17:56
November 22nd 2024, 2:40:00
am
128.72
Ganymede
November 15th 2024,
12:31:00
18’:13’
November 23rd 2024, 1:42:00
am
182.2
Castillo
November 30th 2024,
8:52:57
December 18th 2024, 18:36
441.66
Table 4
Moon
Orbital period in I.M.
(orbital period/ Io orbital period)
Io
1.0
Europa
2.59
(128.72/49.63)
Ganymede
3.67
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(182.2/49.63)
Castillo
8.9
(441.66/49.63)
Table 5
Moon
Distance of moon from center
of Jupiter, in I.U.
Orbital period in I.M.
Io
1.0
1.0
Europa
1.66
2.59
Ganymede
2.44
3.67
Castillo
4.68
8.9
Graph plot which relates to Table 5
Table 6
Moon
Distance of moon
from center of
Jupiter, in I.U.
Orbital period in
I.M.
Distance Cubed
(Distance*Distan
ce*Distance)
Period Squared
(Period*Period)
Io
1.0
1.0
1.0
1.0
Europa
1.66
2.59
4.57
6.71
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Ganymede
2.44
3.67
14.53
13.47
Castillo
4.68
8.9
102.5
79.21
Final Question:
When observing the graph plot it appears that the data points align closely with a linear
trend, therefore suggesting a correlative relationship consistent with Kepler's Third Law.
As mentioned in the instructions, this law posits that the square of a planet's orbital
period is directly proportional to the cube of the semi-major axis of its orbit, and the
plotted moons of Jupiter seem to uphold this principle given that the increase is
constant.
Despite the overall linear trend it is also apparent that the points for Europa and
Ganymede are marginally elevated above the line. This deviation might be attributed to
observational limitations occuring when searching for the extreme position over the
course of different days on the Starrynight software (precision is a challenging aspect to
maintain given the difficulty in keeping track of Jupiter’s localisation). Another factor to
take into consideration are the possible gravitational influences of other nearby moons,
in November, which can induce slight anomalies in one another’s orbital elements
(NASA (3), 2024). Such discrepancies are not unusual in celestial mechanics due to the
complexity of gravitational interactions in multi-body systems, however there’s also no
way for me to verify whetever this hypothesis was the catalyst for the data points' slight
abnormalities.
Nonetheless, let’s keep in mind that the slight divergence from a perfect linear
alignment does not necessarily contradict Kepler's Third Law. Rather, it reflects the
nuanced dynamics of celestial orbits and observational limitations, where minor
variations are both normal and expected in real-world data, therefore affirming that the
law remains applicable even when faced with slight inconsistencies in the data.
Sources:
“Great Wall of China.”
Encyclopædia Britannica
, Encyclopædia Britannica, Inc., 1 Feb.
2024, www.britannica.com/topic/Great-Wall-of-China. Accessed 12 Feb. 2024.
“How Big Is the Great Wall of China.”
Great Wall of China Size
, 1970,
www.chinadiscovery.com/great-wall/facts/how-big-is-the-great-wall-of-china.html.
Accessed 12 Feb. 2024.
“What Is the International Space Station? (Grades 5-8).”
NASA (1)
, 7 Feb. 2024,
www.nasa.gov/learning-resources/for-kids-and-students/what-is-the-international-space-
station-grades-5-8/#:~:text=It%20orbits%20Earth%20at%20an,orbits%20Earth%20ever
y%2090%20minutes. Accessed 12 Feb. 2024.
“How Far Away Is the Moon?”
NASA(2)
, 23 July 2021,
spaceplace.nasa.gov/moon-distance/en/#:~:text=Often%20when%20we%20see%20dra
wings,miles%20(384%2C400%20km)%20away. Accessed 12 Feb. 2024.
“Chapter 3: Gravity & Mechanics - NASA Science.”
NASA(3)
,
science.nasa.gov/learn/basics-of-space-flight/chapter3-3/. Accessed 12 Feb. 2024.
Sail Lake Ontario
, www.great-lakes-sailing.com/lake-ontario.html. Accessed 12 Feb.
2024.
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