SCIN261.Lab1
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Jan 9, 2024
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SCIN261 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
.4
.39
.01
2.56%
Venus
.7
.72
.02
2.77%
Earth
1
1
0
0%
Mars
1.6
1.52
.08
5.26%
Ceres
2.8
2.8
0
0%
Jupiter
5.2
5.2
0
0%
Saturn
10
9.5
.5
5.2%
Uranus
19.6
19.2
.4
2.08%
Neptune
38.8
30.1
8.7
28.9%
* 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:
(a)
What do you infer from the general results for the deviation and relative deviation?
The results show an average accuracy of 97.77% when using the Titus-Bode Rule on the
planets leading up to Neptune. I would infer that this rule could be a useful way to find
the general orbital radius of the planets.
(b)
What do you infer from the discrepancy between the actual radius of Neptune’s orbit and
the radius predicted by the Titius-Bode rule?
2
I believe the discrepancy between
the predicted and actual values for Neptune's orbit
shows the limitations and applicability of the Titius-Bode rule.
QUESTION 2:
(a)
How does the Scientific Method determine if something is a law?
The scientific method determines if something is a scientific law by expressing in the
form of a single mathematical equation whether or not a generalized pattern in nature can
be proven.
(b)
Is the Titius-Bode rule a law? Why or why not?
The Titus-Bode rule cannot be considered a scientific law as the equation doesn’t hold
true for every planet. The rule has also not been able to be repeated for all extrasolar
planetary systems. Due to the rule’s inability to predict the distances of all planets it can
be seen as a mathematical coincidence for our solar system.
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).
3
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TABLE 1.4
Planet
Average Radius of
the Orbit
(AU)
(Average Radius of the Orbit)^0.5
(AU)^0.5
Orbital
Velocity
(km/s)
Mercury
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
Neptune
30.10
5.49
5.40
(Average Radius of the Orbit)^0.5 =
GRAPH 1.1
4
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
1.60
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
5
GRAPH 1.2
QUESTION 3:
(a)
Looking at Graphs 1.1 and 1.2, what is the relationship between the average radius and
the orbital velocity?
The graphs show that the higher the average radius, the higher the orbital velocity and
vice versa.
(b)
Is this relationship strong? Explain your answer.
The relationship is constant in both graphs and shows a reduction in the orbital velocity
as there is a reduction in the average radius.
(c)
Write an equation for the relationship shown in Graph 1.2.
QUESTION 4:
(a)
How do your answers to Question 3, including your equation, relate to Kepler’s Third Law?
[hint: you should be using equations and algebra to show how these things are related].
(b)
Discuss why Kepler’s Third Law is considered a “law”?
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