astro201_project2 (1)
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City Colleges of Chicago, Harry S Truman College *
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Course
201
Subject
Astronomy
Date
Dec 6, 2023
Type
docx
Pages
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Uploaded by ChiefMoon10511
Astronomy 201
Fall 2023
PROJECT 2 – GRAVITATIONAL FORCE
Name: Emmanuel Pena
Due: 10/1/2023
Task
: To compare gravitational forces between us and other bodies around us, and between us and
another planet.
Scenario
:
One of the assertions of astrology is that the positions of stars and planets at the time of a person’s birth
determines their personality and future. Unless astrology proposes the existence of other forms of
interactions, the only
known and measurable
force that is possible from such a distance is
gravity
.
What we want to study is the strength of the force of gravity from a celestial body onto an infant, and
then compare that with the force of gravity from a person in the room onto the same infant.
Part A
:
Based on Newton’s law of universal gravity, we know that the force of gravity between two bodies is
given by:
F
g
=
G ×
M
1
×M
2
d
2
where
F
g is the force of gravity between the two bodies
M
1
is the mass of Body 1
M
2
is the mass of Body 2
d
is the center-to-center distance between the two bodies
G
is the universal gravitational constant,
G
= 6.67 x 10
-11
Nm
2
/kg.
Using this, make an estimate of the force of gravity between:
(i)
a newly-born infant with a mass of 4.00 kg and the gynecologist with a mass of 100 kg
standing 0.20 m away;
(ii)
a newly-born infant with a mass of 4.00 kg and the nearest planet to Earth making the
closest approach. This would be the planet Mars, having a mass of 6.42 x 10
23
kg and with a
distance of closest approach of 5.4 x 10
10
m.
Once you have calculated the force of gravity for each situation, compare the values to each other.
Which one is larger, and by how much? The easiest way to do this comparison is to divide one by the
other, such as (Situation i)/(Situation ii).
Please show your calculation and results in your project report.
(i) To calculate the force of gravity between the infant and gynecologist:
Astronomy 201
Fall 2023
Given:
Mass of infant (m1) = 4.00 kg
Mass of gynecologist (m2) = 100 kg
Distance between them (d) = 0.20 m
Gravitational constant (G) = 6.67 × 10^-11 Nm^2/kg^2
Formula:
F_g = G × (m1 × m2) / d^2
Substituting the values, we get:
F_g = 6.67 × 10^-11 × (4.00 kg × 100 kg) / (0.20 m)^2
F_g = 0.000166 N
Hence, the force of gravity between the infant and gynecologist is 0.000166 N.
(ii) To calculate the force of gravity between the infant and planet Mars:
Given:
Mass of infant (m1) = 4.00 kg
Mass of Mars (m2) = 6.42 × 10^23 kg
Distance between them (d) = 5.4 × 10^10 m
Gravitational constant (G) = 6.67 × 10^-11 Nm^2/kg^2
Formula:
Astronomy 201
Fall 2023
F_g = G × (m1 × m2) / d^2
Substituting the values, we get:
F_g = 6.67 × 10^-11 × (4.00 kg × 6.42 × 10^23 kg) / (5.4 × 10^10 m)^2
F_g = 6.22 × 10^13 N
Hence, the force of gravity between the infant and planet Mars is 6.22 × 10^13 N.
Comparing the two values:
(Situation i)/(Situation ii) = F_g1/F_g2 = 0.000166/6.22 × 10^13
Hence, the force of gravity between the infant and planet Mars is significantly larger than the force of
gravity between the infant and gynecologist, by a factor of approximately 3.64 x 10^14.
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Astronomy 201
Fall 2023
Part B
:
Based on what you have done so far, how would you address the claim from astrologists about the
influence of the astronomical bodies at the time of a person’s birth? In particular, which entity in the
room exert more influence on the infant based on the gravitational force alone? Are there any general
conclusion that you can draw out of this exercise? Please write the clearest and strongest argument that
you can.
In the first scenario, the force of gravity between the infant and the gynecologist was calculated to be
0.000166 N, while in the second scenario, the force of gravity between the infant and Mars was
calculated to be 6.22 x 10^13 N. Comparing these values, we can see that the force of gravity between
the infant and Mars is significantly larger than the force of gravity between the infant and the
gynecologist, by a factor of approximately 3.64 x 10^14. However, even with this significant difference,
the gravitational force exerted by both entities is still minuscule in comparison to other forces present in
everyday life.
Therefore, based on the gravitational force alone, it is evident that neither the gynecologist nor Mars has
a significant influence on the infant's well-being or future. The gravitational force exerted by these
astronomical bodies is insignificant compared to the force of gravity exerted by the Earth itself.
From this exercise, we can draw the general conclusion that the force of gravity, even between bodies
with significant mass differences, is relatively weak when the distances involved are large. When it
comes to the influence of astronomical bodies on human life, the gravitational force alone cannot
explain the claims made by astrologists regarding the impact of celestial positions at the time of birth on
personality or future outcomes.
Rubric for Project 2
7 points
5 points
3 point
0 point
Part A
Correct
calculations
showing clear
work and proper
units.
Correct
calculations. Work
shown unclear or
incomplete.
Missing or
incorrect units.
Calculations
incorrect.
No submission.
Part B
Very clear and
compelling
argument based
on calculation
made in Part A.
Weak or unclear
argument, does
not make
compelling case.
Argument
unconvincing, or
insufficient effort
devoted to
making a rational
argument.
No submission.
6 points
4 points
2 points
0 point
Style,
presentation, and
language.
Clear,
professional,
presentation, use
of proper
Average
presentation,
does not use
mathematical
Lacking in clarity
and difficult to
follow.
Numerous errors
No submission.
Astronomy 201
Fall 2023
mathematical
formatting. No
significant issues
with structure and
composition.
formatting. Good
composition with
a few minor
issues.
and issues with
spelling, grammar,
or structure.
Maximum possible points: 20
**************************
Write your report below
******************************