Introduction to Planetary Science Lab 4
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Jan 9, 2024
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INTRODUCTION TO PLANETARY SCIENCE
Lab 1: Planetary Orbits
INTRODUCTION
The Scientific
Observation
is the key tool of a scientist. It helps a researcher to identify promising aspects of natural phenomena, formulate the right questions and search for answers. Inference
is a logical explanation or conclusion based on observations. It is a main component of the
Scientific Method. In this lab we will explore the differences between the scientific observation and inference through the study of observed properties of the planets of the Solar System. 1.1. - The Titius-Bode Rule a)
Evaluate the expression a = (n + 4)/10 for the values 0, 3, 6, 12, 24, 48, 96, 192 & 384 and fill the blank cells in table 1.1 (below). TABLE 1.1 n a 0 0.4
3 0.7
6 1
12 1.6
24 2.8
48 5.2
96 10
192 19.6
384 38.8
b)
An Astronomical Unit (AU) is approximately the mean distance between the Earth and the Sun. It is a derived constant and used to indicate distances within the solar system. 1
AU = 149,597,870.691 kilometers Fill the blank cells in table 1.3 (Using your previous results and data from table 1.2) and calculate the average relative deviation. 1
TABLE 1.2 TABLE 1.3 Planet a Average Radius of Orbit (AU)
Deviation*
Relative Deviation**
Mercury 0.4
0.39
0.01
0.026
Venus 0.7
0.72
0.02
0.028
Earth 1.0
1.0
0
0
Mars 1.6
1.52
0.08
0.053
Ceres 2.8
2.8
0
0
Jupiter 5.2
5.2
0
0
Saturn 10
9.5
.5
0.053
Uranus 19.
6
19.2
.4
0.021
Neptune 38.
8
30.1
8.7
0.29
* Deviation = |a-Average Radius of Orbit|; this is an absolute value, i.e. no negative numbers. **Relative Deviation = (Deviation/Average Radius of Orbit) * 100% QUESTON 1:
What do you infer from the general results for the deviation and relative deviation? What I notice here is there is varying discrepancies between the deviation amounts. Relative Deviation appears to be more consistent planet to planet than the deviation column. Some differences are very minor as seen with Mercury and Venus. Some results like Earth, Mars and Ceres are equal for both, while others are larger as is the case with Jupiter, Saturn, Uranus and Neptune is the largest. I can infer from this that consistency is not present and results may be unreliable.
2
QUESTION 2:
What do you infer from the discrepancy between the actual radius of Neptune and the radius predicted by the Titius-Bode rule? Is this rule a “law”? How do your answers fit with the Scientific Method? The Titus-Bode rule summarized says that each planet is twice as far from the sun as the previous one. Based on this I infer that the Titus - Bode rule is flawed. While the other planets are close to their respective Titus - Bode estimations, Neptune is farther off than its estimate by a large amount compared to its peers with fractional differences. It is for this reason I would say the Titus-bode rule is not a law and should be used as more of a guide then a set-in stone law. With that said I do not think it is suitable for the scientific method because it is proven to be inaccurate. Instead, it is more suggestive of a scientific hypothesis since it does not meet the definition of scientific law. 1.2. – Kepler’s Third Law Graphing is a pictorial way of representing relationships between various quantities, parameters, or measurable variables in nature. A graph basically summarizes how one quantity changes if another quantity that is related to it also changes. Frequently you do not know the exact relationship and interdependence between the various quantities that are being measured and a graph can give you an idea about how these variables change relative to one another. a)
Fill the blank cells on table 1.4 and create a graph of (Average Radius of the Orbit)^0.5 vs.
Average Orbital Velocity (graph 1.1). TABLE 1.4 Plane
t Average Radius of
the Orbit (AU)
(Average Radius of the Orbit)^0.5 (AU)^0.5
Orbital Velocity (km/s)
Mercur
y 0.39 0.62
47.9
Venus 0.72 0.85
35.0
Earth 1.00 1
29.8
Mars 1.52 1.23
24.1
Jupiter 5.20 2.28
13.1
Saturn 9.54 3.09
9.70
Uranus 19.18 4.38
6.80
3
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Neptun
e 30.10 5.49
5.40
(Average Radius of the Orbit)^0.5 = GRAPH 1.1 0
1
2
3
4
5
6
0
10
20
30
40
50
60
Graph 1.1 Made in Excel
(Average Radius of the Orbit)^0.5 X (AU)^0.5 Orbital Velocity (km/s)
b)
Fill the blank cells on table 1.5 and create a graph of 1/(Average Radius of the Orbit)^0.5 vs. Average Orbital Velocity (graph 1.2). TABLE 1.5 Planet Average Radius of
the Orbit (AU)
1/(Average Radius of the Orbit)^0.5 1
/ (AU)^0.5
Orbital Velocity (km/s)
Mercury 0.39 1.61
47.9
Venus 0.72 1.18
35.0
Earth 1.00 1
29.8
Mars 1.52 0.81
24.1
Jupiter 5.20 0.44
13.1
Saturn 9.54 0.32
9.70
Uranus 19.18 0.23
6.80
Neptune 30.10 0.18
5.40
4
GRAPH 1.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0
10
20
30
40
50
60
Graph 1.2 Made in Excel
1/(Average Radius of the Orbit)^0.5 X 1/(AU)^0.5 Orbital Velocity (km/s)
QUESTION 3:
What can you infer from Graphs 1.1 and 1.2? What is the relationship between the average radius and the orbital velocity based on these graphs? Write an equation that describes this relationship shown in Graph 1.2. Both graphs show a result of the square orbital velocity is reciprocally proportional to the average radius. We can infer in 1.1 that the higher the average radius the slower the orbital velocity. I take this to show larger planets orbit slower (take longer) than smaller planets
Graph 1.2 is liner meaning we can use the slope formula to show the relationship between x (Average Radius) and y (Orbital Velocity). The formula for slope is m = Rise / Run = y2 – y1 / x2 – x. we can solve using two points (0.18, 5.40) and (0.23, 6.80) to get y = 28x + 0.36
QUESTION 4:
How do your answers to question 3 relate to Kepler’s Third Law? Discuss why is Kepler’s Third Law considered a “law”? Kepler’s 3
rd
law says that the square of the orbital period of a planet is proportional to the cube of the semi major axis of its orbit. The equation we solved for in question shows a relationship between inverse proportionality of the square of the orbital velocity and the cube of the semi major axis of the orbit.
5
I think Kepler’s third law is law as it has been demonstrated to hold up to repeated experimentation and predicts
observations mathematically with accuracy. It has been extensively tested and confirmed since its inception. This meets the definition of scientific law vs Titus-Bode which more resembles a scientific hypothesis.
6
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