HW5-AS105_Fall2021
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Astronomy
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Jan 9, 2024
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AS 105
|
Hermes
|
Homework Assignment 5
|
Due Monday 6 Dec. 2021
Please write up your answers in a Word/Google document (you can download the
assignment Word document from Blackboard) and print as PDF, to upload to Blackboard
using Turnitin. You may work with other students in class on this assignment, but your
answers
must
be in your own words.
Motivation:
This homework explores the dynamics of solar systems, as well as the
utility in the search for intelligent alien life by exploring the Drake equation.
This
assignment is meant to familiarize you with the Drake equation before we dis-
cuss it in lecture.
1. Super Planet Crash (
http://www.stefanom.org/spc/
)
simulates the future
evolution of close planetary systems based on gravitational interactions. Start by
clicking on “
Design your own system
” at the top left of the options. The goal of the
game is to make a planetary system of your own creation be stable (i.e. no planet is
ejected, or collides with another body). The challenge is to fit as many massive
objects as possible inside 2 AU (twice the distance between the Earth and the Sun),
teetering close to instability but lasting at least 500 years.
Create your most extreme
solar system. What is your high score? Take a screen shot of your high-score
system (with the score) and embed it into Homework 5.
2. The Drake equation
(written by Frank Drake in 1961) is an order-of-magnitude
tool to
estimate the number of
communicative extraterrestrial civilizations in the
Milky Way
. The original Drake equation has seven terms:
N
=
R
∗
⋅
f
p
⋅
n
e
⋅
f
L
⋅
f
i
⋅
f
c
⋅
L
Page 1 of 3
where:
N
=
the number of civilizations in our Galaxy with which might be able to communicate
R
∗
=
the average rate of star formation in our Galaxy
f
p
=
the fraction of those stars that have planets
n
e
=
the average number of planets that can potentially support life, per star that has
planets
f
L
=
the fraction of planets that could support life that actually develop life at some point
f
i
=
the fraction of planets with life that actually go on to develop intelligent life (civiliza-
tions)
f
c
=
the fraction of civilizations that develop a technology that releases detectable signs of
their existence into space
L
=
the length of time for which such civilizations release detectable signals into space
Multiplying out all these terms could lead to a very small or a very large number.
Our ability to estimate each of the terms has greatly improved since 1961.
Please answer the following:
2. For each term of the Drake equation, Frank Drake and his colleagues ventured
their best "educated guesses" at the seven parameters in 1961. Those values were:
R
∗
= 1 yr
−1
(1 star formed per year, on average, over the life of the Galaxy)
f
p
= 0.35 (one fifth to one half of all stars formed will have planets)
n
e
= 3 (stars with planets will have 1 to 5 planets capable of developing life)
f
L
= 1.0 (100% of these planets will develop life)
f
i
= 1.0 (100% of which will develop intelligent life)
f
c
= 0.15 (10–20% of which will be able to communicate)
L
= 100,000 (civilizations will last somewhere between 1000 and 100,000,000 years)
Using those values, calculate
N
, the estimate of the number of civilizations in our
Galaxy
with which communication might be possible by Drake in 1961. If the
Milky Way has roughly 200 billion stars, using this value of
N
, what is the
chance that a random star in our Galaxy has a civilization that can communicate?
Does that number seem high or low to you?
3. If you consider that our Galaxy is one of roughly 200 billion galaxies in the
observable Universe,
use your answer for
N
from above to estimate how many
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