Task Master:
All the Tasks are linked here so that you can find them in the context of
the lab narrative---which is useful
when completing your Report Form
for IPI
or just working through the Tasks
for RMI.
- Task 1: Best Celestial Sphere Video Ever.
- Task 2: The Sidereal Rotation Period.
- Task 3: Great Circle, Small Circle.
- Task 4: The Horizon.
- Task 5: Circumpolar Objects.
- Task 6: Specific Equatorial Coordinates.
- Task 7: Specific Declinations.
- Task 8: The Southernmost Bright Star
(IPI only).
- Task 9: The Ecliptic.
- Task 10: The Ecliptic Axis.
- Task 11: The Sun's Angular Velocity.
- Task 12: Today's Sun Constellation.
- Task 13: The Changing Night Sky.
- Task 14: Sunrise Calculation.
Optional at the discretion of the
instructor.
- Task 15: Horizontal Coordinates.
- Task 16: Equinox, Solstice.
- Task 17: The North Celestial Pole.
Optional at the discretion of the
instructor.
- Task 18: Altitude on the Meridian.
Optional at the discretion of the
instructor.
- Task 19: Intensity.
- Task 20: Seasons. Optional at the discretion of the
instructor.
- Task 21: The Seasons and Equinoxes/Solstices.
- Task 22: Equinox/Solstice Dates.
- Task 23: Axial Precession.
Optional at the discretion of the
instructor.
- Task 24: Updating Equatorial Coordinates.
Optional at the discretion of the
instructor.
- Task 25: Naked-Eye Observations
(RMI only).
End of Task
- Task 1: Best Celestial Sphere Video Ever:
Sub Tasks:
- View
Celestial Sphere | 1:45:
Best celestial sphere video ever!!!
Note it is a silent movie.
- Have you viewed it?
Y / N
End of Task
- Task 2: The Sidereal Rotation Period:
Why is the physical rotation period of the
Earth relative to the
inertial frame of the
fixed stars
(i.e., the
sidereal day = 86164.0905 s
= 1 day - 4 m + 4.0905 s (on average))
SHORTER than the
solar day = current mean value 86400.002 s
(i.e., the solar noon to
solar noon period)?
Answer in sentences with reference to the figure below
(local link /
general link: sidereal_solar_time_2.html).
HINT: You have to consider the Earth's
revolution around the Sun.
Answer:
End of Task
- Task 3: Great Circle, Small Circle:
What is a great circle?
What is a small circle?
Answer in sentences.
Answer:
End of Task
- Task 4: The Horizon:
The horizon
is a _________________ circle on the celestial sphere.
End of Task
- Task 5: Circumpolar Objects:
Sub Tasks:
- Circumpolar objects
_________________________ set.
- Whether an astronomical object is or is
NOT circumpolar depends on your
_______________________________.
HINT: The figure below
(local link /
general link: declination_altitude.html)
might stimulate your memory.
End of Task
- Task 6: Specific Equatorial Coordinates:
Fill in the blanks below:
- vernal equinox
RA = _____________________
-
celestial equator
Dec = _____________________
-
NCP
Dec = _____________________
-
SCP
Dec = _____________________
-
Polaris
Dec = _____________________
End of Task
- Task 7: Specific Declinations:
By eye-balling the
celestial globe
(if the instructor
remembered to put it out for you) or the
sky map shown in the figure above
(local link /
general link: sky_map_all_sky.html),
what is the approximate average
declination (Dec or δ) of:
- Ursa Minor? _____________________
- Orion? _____________________
- Pyxis? _____________________
End of Task
- Task 8: The Southernmost Bright Star
(IPI only):
Using
TheSky
find the southernmost
star
(i.e., the star closest to the
SCP) with
TheSky
reference magnitude
(which must be close to
the apparent V magnitude)
brighter (i.e., less) than or equal to 3.00 (i.e., ≤ 3.00).
What is its:
- Bayer designation?
_____________________
- apparent V magnitude?
_____________________
- declination?
_____________________
End of Task
- Task 9: The Ecliptic:
Complete the following sentences:
- The ecliptic plane
cuts the celestial sphere
in half by a great circle
called the _____________________ .
- The zodiac constellations straddle
the _____________________ .
- Since the planets
and many other Solar System
bodies orbit nearly in the
ecliptic plane,
those bodies move on celestial sphere
on paths that are very near the _____________________ .
End of Task
- Task 10: The Ecliptic Axis:
Sub Tasks:
- The
Earth's axial tilt
is tilted from the
ecliptic axis by
angle _____________________ .
- The ecliptic is tilted from the
celestial equator by
angle _____________________ .
End of Task
- Task 11: The Sun's Angular Velocity:
Sub Tasks:
- What is the angular velocity
in degrees per
days
of the Sun
on the ecliptic?
Use the
sidereal year = 365.256363004 days (J2000)
and give the result to
6-digit precision.
__________________
-
Which way is the Sun moving? __________________
- The ancient Babylonian astronomers
chose to divde the circle into 360 units that we
call degrees.
They could have chosen 60 units or 100 units or 129 units or 180 units or 365.25 units.
Given that they were studying the
Sun's motions, what is one possible reason for
choosing 360 units?
Answer in sentences.
Answer:
End of Task
- Task 12: Today's Sun Constellation:
Sub Tasks:
- In what zodiac constellation
is the Sun today?
To find out, use the applet figure below
(local link /
general link: naap_zodiac.html)
(if it is working (which it probably is NOT),
TheSky,
or
the celestial globe
set out on your bench (if the
instructor
remembered to do this).
What zodiac constellation
transits
the meridian at about
midnight?
Answer:
- The zodiac signs are actually
NOT the zodiac constellations.
The zodiac signs are, in fact,
30° segments of the ecliptic
named for the constellation
they contained circa 500 BCE
when the Babylonian astronomers
were still developing astrology---for fun and profit.
The zodiac signs start from the
vernal equinox.
Due to the axial precession
(see section Axial Precession),
the vernal equinox has moved westward since
500 BCE and the
zodiac signs NO
longer contain or at least NOT much
of the constellations
they are named for.
What zodiac sign
contained the Sun when you
(or your group leader if appropriate) were born (i.e., what is
your zodiac sign)
and what
zodiac constellation
contained the Sun when you
(or your group leader if appropriate) were born?
See
Wikipedia: Zodiac: Twelve signs
(Table of Dates: Scroll down ∼ 5%)
(in the column for
tropical zodiac)
and
Wikipedia: Zodiac: Constellations
(Table of Dates: scroll down ∼ 5%)
(in the column for
IAU boundaries).
Answer:
End of Task
- Task 13: The Changing Night Sky:
How the night sky changes
as the Sun moves along the
ecliptic is explicated in
the figure below
(local link /
general link: zodiac_ecliptic.html)
this task
and applet figure above
(local link /
general link: naap_zodiac.html)
this task
(if it is working which it probably is NOT).
Sub Tasks:
- Study
the figure below
(local link /
general link: zodiac_ecliptic.html)
this task
and applet figure above
(local link /
general link: naap_zodiac.html)
this task
and push all the buttons
on the applet.
(If the applet is NOT working omit applet aspect of this sub task.)
Have you done this? Y / N
- Because of the Sun's
motion along the ecliptic
(and therefore relative to the
fixed stars),
the fixed stars
rise (earlier/later) every day.
Answer: ___________________ .
- The
night sky
(i.e., that half of the
celestial sphere
OPPOSITE the Sun)
shifts eastward
on the celestial sphere
about _____ degree per day.
- Draw a labeled diagram with the
Earth at the center illustrating the motion of the
night sky
on celestial sphere
during the course of a year.
Explicate the diagram.
HINT: See the figure below
(local link /
general link: zodiac_ecliptic.html).
Answer:
End of Task
- Task 14: Sunrise Calculation:
Sub Tasks:
- Use the approximate sunrise formula given above
to calculate the sunrise
for today's date:
2025 August 17, Sunday
You will have convert today's date in to month count from the beginning of the
year with the
decimal fraction included.
For example, if it is June 21, t_month ≅ 5.67.
In your answer, you will have to convert time from hours to hours and minutes.
Answer:
- Compare your answer in Sub Task 1 to the
accurate and precise time
given by USNO: Sun or Moon Rise/Set Table for One Year
(offline in
2020 for awhile)
or
google
"sunrise time".
What is the error in minutes?
Answer:
End of Task
- Task 15: Horizontal Coordinates:
Sub Tasks:
- Why are
horizontal coordinates
(altitude and
azimuth) useless
for catalogs of locations for
astronomical objects?
Answer in sentences.
Answer:
- What are
horizontal coordinates good for?
Answer in sentences.
Answer;
End of Task
- Task 16: Equinox, Solstice:
Sub Tasks:
- Study the figure and applet in the subsection
above and push all the buttons
on the applet.
(If it is working which it probably is NOT. If NOT omit this sub task.)
Have you done this? Y / N
- Where is the Sun
on the celestial sphere on
an equinox day? ________________________
- Where does the Sun
rise and set on the horizon
on an equinox day? ________________________
- How long are daytime and
nighttime on
an equinox day? ________________________
- Qualitatively where does the Sun
rise and set on the horizon
in June? ________________________
Northern Hemisphere,
which is longer day or
night on this day? ________________________
- Qualitatively where does the Sun
rise and set on the horizon
in December? ________________________
In the Northern Hemisphere,
which is longer day or
night on this day? ________________________
- If the stars during the course of
a day follow paths that are
parallel to the
horizon, you are where?
__________________________________ .
- Where on Earth are
day and
night always 12 hours long?
__________________________________
HINT: What
latitude circle
is always cut in half by the
Earth's
terminator.
End of Task
- Task 17: The North Celestial Pole:
Sub Tasks:
- Using a labeled diagram show that
altitude from
due north
of the north celestial pole (NCP)
AN(NCP)
is given by the formula:
AN(NCP) = L ,
where L is latitude
(counted as negative if
south latitude)
and the AN(NCP) is counted as negative if the
NCP is
below the horizon.
Diagram:
HINTS:
- The NCP
and the celestial equator
are so remote
that starting from the
Earth's surface
all lines to the
NCP
are parallel
and all lines to the
and celestial equator
are parallel.
A line to the NCP
a line to the celestial equator
starting from the Earth's surface
are always perpendicular
- You will need to draw the Earth in cross section.
From a general point on the surface, draw lines to the
NCP
and the celestial equator
- From the Earth's center draw a radius line
through the general point and extending well beyond it and draw a line
to the celestial equator.
- Draw a line tangent to the
Earth's surface.
- Imagine rotating the
right angle
formed by the
NCP
and the celestial equator
lines at the general point into the
north side of the tangent line.
- What is the altitude
of the NCP in
Las Vegas, Nevada or whatever
location you happen to be in? _________________________
- For the Northern Hemisphere,
how close to the NCP in
angle
does an astronomical object
have to be circumpolar
for your location? Why? What is the constraint on the
declination
of the astronomical object?
HINT: The figure below
(local link /
general link: sky_swirl_polaris_animation.html)
from
Lab 1: Constellations might stimulate your memory.
Answer:
- What constellations
are on average
circumpolar
for your location? HINT: Make use of the
all-sky sky map given above or
TheSky.
See also the figure below
(local link /
general link: sky_swirl_polaris_animation.html).
Answer:
End of Task
- Task 18: Altitude on the Meridian:
The general formulae relating
altitude AN/S
(upper/lower case for altitude
from due north/due south)
along the meridian,
declination (δ),
and latitude (L)
(with southern latitudes counted as
negative numbers)
are:
AN/S = (±)N/S(L - δ) + 90°
δ = L +(±)N/S(90° - AN/S)
L = δ +(±)N/S( AN/S - 90°)
For proof of these formulae, see the figure above
(local link /
general link: declination_altitude.html).
Sub Tasks:
- What is the
altitude of
NCP/SCP
from due north/due south?
HINT: You have to specialize the 2nd general
formula above
for the
declination
of the
NCP/SCP
for due north/due south.
Answer:
- What is the declination
of zenith for any
latitude?
Answer:
- You are at sea
doing celestial navigation
with your brass
sextant.
On an equinox day at time ______________,
the Sun
transits the meridian
at zenith.
What is your latitude
and where are you?
Answer:
- The general
formulae are proven
in the figure below
(local link /
general link: declination_altitude.html).
Is the proof intelligible to you?
You get the mark, whatever your answer.
Y / N
End of Task
- Task 19: Intensity:
Sub Tasks:
- What is the area formula
for a circle of
radius R? ____________________
- What is the surface area formula
for a sphere
of radius R? ____________________
- The power absorbed by a non-reflecting sphere of radius R
from a beam of intensity I impinging on it from one direction is
IπR**2.
What is the formula for
the average power per unit surface area absorbed by the
sphere counting the whole
sphere surface area?
____________________
End of Task
- Task 20: Seasons:
Sub Tasks:
- What is the short answer for why the
Earth has
seasons? Answer in sentences.
Answer:
- The
Earth's orbit
has an eccentricity
of 0.0167.
This means that the Earth's
distance from the Sun
varies up and down from the
mean orbital radius by
1.67 %.
perihelion is occurs
about Jan03 and
aphelion about Jul04
(see Wikipedia: Earth's orbit: Events in the orbit).
Does the eccentricity
of the Earth's orbit
have any effect on the Earth's climate?
Explain.
Answer:
-
Explain why the Sun never sets
at the North Pole in
Northern-Hemisphere summer and never rises
in Northern-Hemisphere winter.
What is the situation at the South Pole?
HINT: You can refer to the diagrams above.
Answer:
End of Task
- Task 21: The Seasons and Equinoxes/Solstices:
Sub Tasks:
- The astronomical events that mark the beginning of the
seasons are
__________________,
__________________,
__________________,
and
__________________.
Note the terms
solstice and equinox
have two meanings: one is the event and the other
is the place on the
celestial sphere
where the event occurs.
- Find the
solstice and equinoxe
on the all-sky sky map.
Have you done this? Y / N
End of Task
- Task 22: Equinox/Solstice Dates:
Fill in the data in the table below following the instructions below.
- For fiducial date, just use the 21st of the appropriate
calendar month.
Click on the name of the event for the appropriate
calendar month.
- For the equatorial coordinates of the
solstices and equinoxes
on the celestial sphere,
see
Wikipedia: Equinoxes and solstices
for their right ascensions (RA)
and think about the
Earth's axial tilt
23.4° for declinations (Dec).
- For the last column, you will have to use the general formula proven in the figure at
local link /
general link: declination_altitude.html.
This general formula for the
altitude of
an astronomical object
on the meridian
of the celestial axis is
AN/S = 90°+(±)N/S(L-δ) ,
where the upper/lower case is for
altitude from
due north/due south,
L is the local latitude
(counting southern latitudes as negative),
and δ is the declination (Dec)
of the astronomical object.
For the last column, you will need the lower case
(i.e., AS = 90°-N/S(L-δ))
since the
Sun at an
altitude measured from
due south.
Two-digit precision suffices.
_____________________________________________________________________
Table of Solstice and Equinox Data
_____________________________________________________________________
Sun Position Fiducial Date RA Dec Altitude of the Sun
(h) (degrees) in Las Vegas at
Solar Noon
(degrees)
_____________________________________________________________________
vernal equinox
summer solstice
fall equinox
winter solstice
_____________________________________________________________________
End of Task
- Task 23: Axial Precession:
Sub Tasks:
- The
sidereal year = 365.256363004 days (J2000),
where the epoch is
J2000.0.
This is the period it takes the
Earth to orbit
the Sun
eastward
relative to the inertial frame of the
fixed stars.
This is the "physical"
orbital period.
What is the angular velocity in degrees per day of the
Earth? R_e = _________________________
- The
axial precession period
is ∼ 26000 year.
The exact value is NOT known since the rate of
axial precession
is subject to many small
gravitational perturbations.
However, assuming the current rate of
axial precession
were constant, the
axial precession period
would be about 25,771.5 Julian years (Jyr)
(see Wikipedia: Axial precession: Values).
Note a Julian year is exactly 365.25 days.
Using the exact period result
25,771.5 Julian years, what is the
angular velocity in degrees per day of
vernal equinox
westward along the
ecliptic? R_v = _________________________
-
From the Earth's perspective,
both the Sun
and vernal equinox
(carried along by the precession
of the celestial equator
carried along by the
Earth's axial precession)
are moving along the ecliptic.
The Sun
moves eastward
and
the vernal equinox
moves westward.
Let's take eastward as positive
and westward as negative.
So the angular velocity of the
vernal equinox is minus the value you calculated above
(i.e., R_v = - |R_v|).
The time t for the Sun to lap the
vernal equinox satisfies
the equation
360° = (R_e - R_v)t
What is t in days?
Since the answer requires
double-precision math,
we will just give the result:
Answer: We have
t = 360°/(R_e - R_v) = 360°/(0.985609113115 + 0.0000382448) = 365.2421904276 days.
The accepted
solar year = 365.2421897 days (J2000).
So the two values agree to 8 digit places. The calculation wasn't so bad.
- What is the period calculated in the Sub Task 3 called? _________________________
End of Task
- Task 24: Updating Equatorial Coordinates:
Explain why the equatorial coordinates
for astronomical objects beyond the
Solar System
have to be updated every few years. Give the main reason and a second reason.
Answer:
End of Task
- Task 25: Naked-Eye Observations
(RMI only):
EOF
End of Task
