SCI238Assignment5Solutions - SCI 238 Online - Fall 2023
.pdf
keyboard_arrow_up
School
University of Waterloo *
*We aren’t endorsed by this school
Course
238
Subject
Physics
Date
Dec 6, 2023
Type
Pages
4
Uploaded by JusticeElectronNarwhal14
©
Michel
Fich,
2023
SCIENCE
238
Assignment
#5
(Requires
course
material
up
to
and
including
Module
6e)
1)
Abinary
star
system
is
observed.
(a)
The
stars
are
0.8
arcsec
apart
and
orbit
with
a
period
of
12.0
years.
If
the
stars
are
10
parsecs
from
the
Sun
then
what
is
the
mass
of
these
two
stars
(together)?
Assume
circular
orbits.
(b)
If
one
of
the
stars
is
three
times
as
bright
as
the
other
AND
Stellar
luminosity
is
related
to
stellar
mass
by
L
o<
M3
then
what
is
the
mass
of
each
of
the
two
stars?
(Marks:
4)
(a)
(2
marks)
The
distance
between
the
stars
is
the
semi-major
axis
given
by
angle
x
distance
which
gives (with
correction
from
arcseconds
to
radians
%810
x
3.086
x
1016
=
206265
and
putting
in
parsecs
in
meters)
a
=
1.2x10?m
=8.0A4.U.
am?
G(my+mg)
plus
constants:
(12.0
X
365.25
X
24
X
60
X
60)?
=
2
m(1.20
X
10'2)3
which
then
gives
m;
+m,
=
7.13
x
10*°kg
or
3.59
Mgy,
[Note:
the
mass
of
the
Sunis
Mg,
=
1.989
x
103%kg].
Rounding
this
is
3.6Mg,n
e
Alternative
(partial)
solution:
(my
+
my)P2(yr)
=
a3(A.U.)
=
(my
+my)122
=8.0°=
m,
+
m,
=
3.56
Mgy,
=
3.6Mgyn
Note
on
significant
figures.
Because
the
angle
is
only
given
to
1
digit
accuracy
(0.8)
the final
answer
of
3.6
could
be
rounded
to
4.0
here.
But
keep
an
extra
digit
or
two
in
order
to
do
the
calculations
in
(b)
e
Kepler's
Third
Law
is
P2
=
a®
and
putting
in
the
values
above
(b)
(2
marks)
Since
brightness
depends
on
luminosity
and
distance,
and
the
stars
are
the
same
distance
from
us,
and
we
can
write
L
(3)3:
3=
(fl)s
and
Ly
my
ms.
my
=
1.44m,.
From
(a):
1.44m,
+
m,
=
3.59Ms,,,
and
m,
=
1.47Mg,,,,.
This
then
gives
my
=
2.12
Mg,,,,.
After
rounding:
my
=
2.1Mg,,,
and
m,
=
1.5Mg,,
Note
on
significant
figures:
students
may
choose
to
round
to
one
digit
and
that
is
fine
as
long
as
the
unrounded
number
is
shown
too
so
that
the
two
stars
have
different
mass.
(Marks:
10
out
of
60
Assignment
Marks)
©
Michel
Fich,
2023
2)
Investigate
the
average
density
of
Main-Sequence
stars.
(a)
Make
a
log-log
plot
of
Mass
versus
Radius
for
spheres
with
constant
densities
of
102
10°
and
10°
kg/m?
and
Masses
between
0.05
Msu,
and
200
Msu,
.
Note
that
this
plot
will
consist
of
four
(changed
to
three
to
simplify
problem)
lines,
one
for
each
density.
(b)
On
the
plot
in
(a)
add
the
Mass
and
Radius
of
the
stars
on
the
Main
Sequence
stars
shown
on
the
table
below
(This
is
a
standard
data
table
taken
from
a
graduate
course
textbook).
(c)
Describe
and discuss any
trends
that
you
see
in
the
figure
produced
above.
(Marks:
6)
(a)
(2
marks)
Mass
is
given
by
M
=
%nR3p
where
p
is
the
density.
To
simplify
the
calculation
of
the
lines
put
in
units
of
kg/m3
for
density
and
Solar
Radii
and
Solar
Masses:
[note
that
Mgy
=
M/Mgyy]
Mgorar
X
1.989
x
1030
=
%nR;,m,(e.957
%
108)3p
and
after
calculations:
or
Mgoiar
=
7.09
X
107*R3
0P
[Note
that
for
density
of
water,
p
=
103,
this
gives
Mg,
1q,
=
0.709R3,
4,
...
a
one
Solar
Radius
sphere
has
a
mass
of
0.709
Solar
Masses]
The
table
below
gives
a
set
of
possible
endpoints
for
the
lines
to
be
drawn
in
the
same
units
as
above.
(Note
that
mass
limits
are
used
here
for
plotting,
but
could
use
radius
to
set
plotting
line
limits.)
p
R
log
(R)
M
log
(M)
10?2
0.89
—0.051
0.05
-1.3
102
141
1.15
200
2.30
103
0.41
—0.38
0.05
-1.3
103
6.56
0.82
200
2.30
10*
0.19
-0.72
0.05
-1.3
10*
3.04
0.48
200
2.30
(Marks:
10
out
of
60
Assignment
Marks)
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Related Questions
3:00 PM Fri 23 Apr
* * ni 26%
web.whatsapp.com
+
blob:https://web.whatsapp.com/d4009cff-8...
G Identify the names of the four major arms of...
W Inflation (cosmology) - Wikipedia
in this water body.
4 of 9
Q.5 Identify the names of the four major arms of Milky way galaxy :
a) Norma and Cygnus, Sagittarius, Scutum-crux, Perseus.
b) Norma and Cygnus, Orion, Scrotum-crock, Perseus.
c) Norma and Clittorus, Sagittarius, Scrotum-crux, Perseus.
d) Norma and Cygnus, Orion , Scutum-crux, Perseus.
Q.6
In a far far away Galaxy lies a solar system untold, wherein, lies the planet, Stephenland
inhabited by Meeseeks (a simple, but sentient species ). Their planet is invaded by the dreaded
Brainiac Titanoids and their minions, P'nados . They started exploiting the natural resources of
the planet at a scale, wherein, it actually started having affecting the mass of the planet. The
mass lost was so huge that the atmosphere of the planet was actually endangered. They're now
facing the threat of a waning…
arrow_forward
1.)How long do you have to wait for a star to undergo its maximum parallactic displacement?
2.) How can the observation of stellar parallaxes in general be used as evidence against a geocentric view of the cosmos?
arrow_forward
1
arrow_forward
Q15. The space observatory Gaia was launched in 2013 as the successor to
Hipparcos and is returning data on its ambitious mission to catalog the 3-
dimensional position of more than 1 billion stars in the Milky Way. The
smallest parallax angle it can measure, for stars of at least magnitude 12, is
0.000008", What is the most distant star to which Gaia can measure parallax?
Q16. The center of our Galaxy is about 8,500 parsecs from Earth.
a. What would be the parallax angle of a star near the center of the
Galaxy?
b. Could this angle be measured by Hipparcos?
c. Could this angle be measured by Gaia?
arrow_forward
Can i get assistance in this physics astronomy question
arrow_forward
G:06)
arrow_forward
2. 60 million years ago, an asteroid hit the Earth and killed every T-Rex on Earth. That
same day, a star was born.
45 years ago, the singer of the band T Rex, Marc Bolan, wrapped himself around a tree
at high speed. That same day, the star born 60 million years ago left the main
sequence. Estimate the mass of that star, stating all assumptions you make.
arrow_forward
I attempted to answer this question and I'm not sure what I am doing wrong. My formula says A.S. = 206265 (separation/distance from observer)
I know to convert to the same units, so I ended up with 80 Million Km being 8 x 10 ^ -6 LY
Could you please explain each step especially for the part that I got wrong for both A and B?
arrow_forward
If our universe is expanding, what are the implications for the separation between two stars within our galaxy?
A.
The two stars are moving farther apart.
B.
The two stars are moving closer together.
C.
The distance between the two stars is unaffected.
D.
The question is impossible to answer without more information.
arrow_forward
Which of the following is FALSE (NOT TRUE)?
A) The Doppler effect can be used to measure the radial velocity of a star.
B) We can measure the distance to galaxies using parallax.
C) Spectroscopy can tell us what a star is made of.
D) Spectroscopy can tell the temperature of a star.
E) Stars are made mostly of hydrogen.
arrow_forward
A star is observed to have a parallax of
0.05". If we were to send a radio signal
towards this star how much time would it
take for the signal to reach the star?
Choose the option below that most
closely matches your answer.
Select one:
а.
75.2 years
O b. 101.4 years
Ос.
55.2 years
O d. 258.1 years
е.
65.2 years
arrow_forward
1. A distant galaxy has an apparent magnitude of 10 and is 4,000 kpc away. What is its absolute magnitude? (Round your answer to at least one decimal place.)
The difference in absolute magnitude between two objects viewed from the same distance is related to their fluxes by the flux-magnitude relation.
FA/FB= 2.51(MB − MA)
2. How does the absolute magnitude of this galaxy compare to the Milky Way
(M = −21)?
arrow_forward
Can you please answer the following questions
The star Sirius has an apparent magnitude of -1.46 and appears 95-times brighter compared tothe more distant star Tau Ceti, which has an absolute magnitude of 5.69.(a) Explain the terms apparent magnitude, absolute magnitude and bolometric magnitude.(b) Calculate the apparent magnitude of the star Tau Ceti.(c) Find the distance between the Earth and Tau Ceti.
arrow_forward
1.) How far, in parsecs, is an object that has a parallax of 1 arc second? How far is it, in light years?
2.) How far in parsecs, is an object that has a parallax of 0.1 arc-seconds? How far is it, in light years?
arrow_forward
Perhaps the most fundamental problem in all of astronomy is the determination of distance to the various objects in the cosmos. Which of the following seems least reasonable regarding the various measurement techniques:
Group of answer choices
The Hubble Law relates the recessional speed of distant objects (measured with the Doppler Effect) to distance.
Hubble law is most useful for determining the distance to nearby objects, while parallax is most useful for the more distant objects.
We can determine the position of a star on the H-R diagram through spectral analysis and then figure out the distance by comparing absolute luminosity (from H-R diagram) to apparent brightness.
The distance to nearby stars can be determined by measuring parallax.
The distance to the planets in our solar can be determined by measuring the time for a radar signal to reach a planet, bounce off, and return.
arrow_forward
Question A1
a)
The Large Magellanic Cloud (LMC) is a galaxy in the vicinity of the Milky Way. It is at a
distance of 50 kpc, and has a size across of 9.86 kpc.
Consider a star similar to Vega (absolute magnitude M = 0.58) which is at the edge of the
LMC as seen on the sky. What is its apparent magnitude? Show your calculation.
b) A second similar star is observed near the centre of the LMC as seen on the sky with an
observed apparent magnitude of m = 20.3. Is this consistent with the star being a member
of the LMC? Explain your reasoning.
c) An observational study has derived a map of the extinction Ay across the LMC, and shown
that its average value is 0.38, with a standard deviation of 0.57.
For the star discussed in part (b), if extinction is taken into account, does your conclusion
about the star's membership of the LMC change? Explain your reasoning. You may assume
that the star may suffer the full (positive) range of extinction found in the study of the LMC.
d) Which other…
arrow_forward
9.
I found this meme online. Its goal is to undermine the picture of the Universe
proposed by modern astronomy as it was discussed in class. How would you answer this
question if you want to convince someone of the validity of the view proposed by modern
astronomy?
THE NORTH STAR POLARIS IS STATIONARY
AND NEVER MOVES
fb.com/fematters
HOW IS THIS POSSIBLE
ON A SPINNING BALL HURLING THROUGH SPACE?
arrow_forward
Given that a pair of stars are found to be orbiting each other with a period of 11.86
[yrs] and a separation of 5.2 [AU], what is the binary star system's total mass (i.e.-
M1+M2) expressed in units of our Sun's mass?
a) 61.7
b) 39.5
c) .0162
d) 1
e) 1.0 x 10^30
arrow_forward
M6
arrow_forward
5. A planet of mass m is located on a line equidistant from two
identical stars of mass M, located at I = +d, as shown.
a) Obtain the equation of motion of the planet.
b) Describe the motion (in words).
M
M
arrow_forward
a) Calculate the period of the solar system's orbit around the Milky Way. Assume that we are 8.5
kpc from the galactic center and assume that the mass of the Milky Way interior to our orbit is
~ 10¹¹ solar masses.
Alpha Centauri is a multiple star system only 1.34 parsecs away. The apparent magnitudes of the
two main stars are:
a Cen A: my = +0.01;
a Cen B: my = +1.33.
b) Calculate the ratio of the flux we receive in the V filter from a Cen A to the flux we receive
from a Cen B.
c) Calculate the absolute magnitude My of a Cen B.
arrow_forward
#1 H
arrow_forward
help asap
arrow_forward
I am trying to calculate the gravitational mass (in solar masses) I have the formula M= V^2 R / G (4.31 x 10^-6) The paperwork says our numbers should be big but I am coming up with .002 etc. What am I doing wrong?
arrow_forward
Using MBH
=
6.6 × 10 Mo, calculate the below.
a. Find radius of the Schwarzschild sphere (Schwarzschild radius Rs). You
can calculated from the appropriate formula or just use the fact that for
an object of 1 solar mass Rs = 3 km.
b. Express Rs in km, in AU, in parsecs.
c. Using the distance to M87 and your result above, find angular radius of
the SMBH (Schwarzschild radius). Express it in arcseconds (") and micro-
arcseconds (pas)
d. Take the radius of Pluto's orbit equal to 40 AU and find its angular size
(in micro-arcseconds, pas) at the distance of M87.
arrow_forward
Ignore the part where it says Numbers
My question is with what did they substitute r1 with?
arrow_forward
1. What would be the diameter (of the event horizon) of a black hole with the same mass as Jupiter?
(2 points)
answer: D
BH
ft
m =
arrow_forward
SEE MORE QUESTIONS
Recommended textbooks for you
Horizons: Exploring the Universe (MindTap Course ...
Physics
ISBN:9781305960961
Author:Michael A. Seeds, Dana Backman
Publisher:Cengage Learning
An Introduction to Physical Science
Physics
ISBN:9781305079137
Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres
Publisher:Cengage Learning
Related Questions
- 3:00 PM Fri 23 Apr * * ni 26% web.whatsapp.com + blob:https://web.whatsapp.com/d4009cff-8... G Identify the names of the four major arms of... W Inflation (cosmology) - Wikipedia in this water body. 4 of 9 Q.5 Identify the names of the four major arms of Milky way galaxy : a) Norma and Cygnus, Sagittarius, Scutum-crux, Perseus. b) Norma and Cygnus, Orion, Scrotum-crock, Perseus. c) Norma and Clittorus, Sagittarius, Scrotum-crux, Perseus. d) Norma and Cygnus, Orion , Scutum-crux, Perseus. Q.6 In a far far away Galaxy lies a solar system untold, wherein, lies the planet, Stephenland inhabited by Meeseeks (a simple, but sentient species ). Their planet is invaded by the dreaded Brainiac Titanoids and their minions, P'nados . They started exploiting the natural resources of the planet at a scale, wherein, it actually started having affecting the mass of the planet. The mass lost was so huge that the atmosphere of the planet was actually endangered. They're now facing the threat of a waning…arrow_forward1.)How long do you have to wait for a star to undergo its maximum parallactic displacement? 2.) How can the observation of stellar parallaxes in general be used as evidence against a geocentric view of the cosmos?arrow_forward1arrow_forward
- Q15. The space observatory Gaia was launched in 2013 as the successor to Hipparcos and is returning data on its ambitious mission to catalog the 3- dimensional position of more than 1 billion stars in the Milky Way. The smallest parallax angle it can measure, for stars of at least magnitude 12, is 0.000008", What is the most distant star to which Gaia can measure parallax? Q16. The center of our Galaxy is about 8,500 parsecs from Earth. a. What would be the parallax angle of a star near the center of the Galaxy? b. Could this angle be measured by Hipparcos? c. Could this angle be measured by Gaia?arrow_forwardCan i get assistance in this physics astronomy questionarrow_forwardG:06)arrow_forward
- 2. 60 million years ago, an asteroid hit the Earth and killed every T-Rex on Earth. That same day, a star was born. 45 years ago, the singer of the band T Rex, Marc Bolan, wrapped himself around a tree at high speed. That same day, the star born 60 million years ago left the main sequence. Estimate the mass of that star, stating all assumptions you make.arrow_forwardI attempted to answer this question and I'm not sure what I am doing wrong. My formula says A.S. = 206265 (separation/distance from observer) I know to convert to the same units, so I ended up with 80 Million Km being 8 x 10 ^ -6 LY Could you please explain each step especially for the part that I got wrong for both A and B?arrow_forwardIf our universe is expanding, what are the implications for the separation between two stars within our galaxy? A. The two stars are moving farther apart. B. The two stars are moving closer together. C. The distance between the two stars is unaffected. D. The question is impossible to answer without more information.arrow_forward
- Which of the following is FALSE (NOT TRUE)? A) The Doppler effect can be used to measure the radial velocity of a star. B) We can measure the distance to galaxies using parallax. C) Spectroscopy can tell us what a star is made of. D) Spectroscopy can tell the temperature of a star. E) Stars are made mostly of hydrogen.arrow_forwardA star is observed to have a parallax of 0.05". If we were to send a radio signal towards this star how much time would it take for the signal to reach the star? Choose the option below that most closely matches your answer. Select one: а. 75.2 years O b. 101.4 years Ос. 55.2 years O d. 258.1 years е. 65.2 yearsarrow_forward1. A distant galaxy has an apparent magnitude of 10 and is 4,000 kpc away. What is its absolute magnitude? (Round your answer to at least one decimal place.) The difference in absolute magnitude between two objects viewed from the same distance is related to their fluxes by the flux-magnitude relation. FA/FB= 2.51(MB − MA) 2. How does the absolute magnitude of this galaxy compare to the Milky Way (M = −21)?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Horizons: Exploring the Universe (MindTap Course ...PhysicsISBN:9781305960961Author:Michael A. Seeds, Dana BackmanPublisher:Cengage LearningAn Introduction to Physical SciencePhysicsISBN:9781305079137Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar TorresPublisher:Cengage Learning
Horizons: Exploring the Universe (MindTap Course ...
Physics
ISBN:9781305960961
Author:Michael A. Seeds, Dana Backman
Publisher:Cengage Learning
An Introduction to Physical Science
Physics
ISBN:9781305079137
Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres
Publisher:Cengage Learning