Name: _______________
SUID: ________________
AST 104 Lab 8: Hubble Deep Field
& The Fate of the Universe
Introduction:
One of the most revered images in all of Astronomy is the so called “Hubble Deep Field”
image. Part of the Hubble Telescope’s mission was to use its telescopic power to observe
distant objects that were previously beyond our ability to see. So, after some minor mishaps
involving a bad mirror and some recalibration, the Hubble Telescope was aimed at a “typical”
patch of sky, which was devoid of many bright sources within the Milky Way Galaxy, so that
most if not all of the image would be of distant objects, such as galaxies. Your TA should have
the resulting image on display.
The image is beautiful, not only for its diverse array of colors and shapes, but for what it
reveals about our Universe. The fraction of the sky this represents is incredibly small (You’ll see
just how small in section 1), and yet even within this tiny fraction of the sky, we see many,
many galaxies, each with its billions upon billions of stars, each of which with the possibility for
many planets. It’s humbling in a way to see just how small our corner of the Universe really is.
However, more can be drawn from this image than poetry and existential epiphanies;
this image is enough to make a prediction for the very fate of the Universe itself. This lab will
walk you through how, first by familiarizing you with the use of angular distances to make
measurements of the sky, and then by deducing how many galaxies exist in our Universe, and
then using that result to determine what fate has in store for our Universe.
Part 1: Angular Measurement:
You are likely familiar with the idea of measuring lengths and distances using a ruler or
similar device, obtaining a measurement in units of length such as inches or meters. But this
way of measuring isn’t useful for measuring things we see in the sky. Instead we measure such
things in terms of angles; we state lengths as the angle the object makes in the sky. You can
imagine finding the angle of the Moon by extending your arm so that you point to the bottom
of the moon, and the raising your arm until you point to the top. The angle your arm swept
through is the angular measurement of the Moon.
We’ll be using measurements like this throughout the lab, so we’ll familiarize you with
them by exploring just how small the Hubble Deep Field image really is, first by comparing it to
the familiar Moon, and then to the sky as a whole.
1.) A degree is subdivided into smaller units (In much the same way that feet are divided
into the smaller inches); 1 Degree contains 60 arc-minutes, and 1 arc-minute contains 60
arc-seconds. The diameter of the Moon measured in degrees is about . 5𝑜 . What is the
Moon’s diameter in arc-minutes?
Moons Diameter: ___________ arc-minutes.
1
2.) The area of a circle in terms of its diameter is 𝐴 = 4 𝜋𝐷2 , where D is the diameter. What
is the area of the Moon in arc-minutes^2?
Moon’s Area: __________ arc-minutes^2.
3.) At each table should be a printout of a small section of the Hubble Deep Field image
(Specifically, the top left corner). This image represents roughly 1/13th of the total
image, and is approximately a square with length of .6 arc-minutes. Thus, its area is .36
arc-minutes^2. Based on this, how many times can this small section fit inside the area
of the moon in the sky?
The Hubble Deep Field image can fit in the area of the Moon _________ times!
4.) Based on these answers, do you think the section of the Hubble Deep Field image on the
printout represents a large portion of the sky?
Part 2: The Number of Galaxies in the Universe
When the astronomers controlling the Hubble Telescope selected the region of the sky
to point the telescope at, they intentionally chose a “typical” region of the sky. Thus, it makes
sense to assume that what is true for this part of the sky ought to be true for everywhere in the
sky. We will use this fact to estimate the number of galaxies in the Universe
1.) We can think of the sky as a sphere that encapsulates the Earth, where what we see is
the “interior surface” of that sphere. Thinking of the sky this way, we can deduce the
radius of this sphere to be about 57.3 degrees. Convert the number to arc-minutes, and
then find the area of the sky in arc-minutes using the formula 𝐴 = 4𝜋𝑟 2 . (Note: You
should consider using scientific notation for the rest of this lab. The numbers get quite
messy otherwise!)
The Area of the sky is _____________ arc-minutes^2.
2.) How many of the Deep Field Image sub-sections would we need to cover the entire sky?
Consider using scientific notation.
We would need ____________ Deep Field images to cover the entire sky.
3.) Carefully count the number of galaxies in the printout of the small piece of the Hubble
Deep Field image.
Number of galaxies in Deep Field Image sub-section: ____________ galaxies.
4.) Using your answers to questions 2 and 3, find a way to estimate the total number of
galaxies in the Universe. It is worth noting how impressive this number is, both because
of how many galaxies this reveals to be in the Universe, and because such an estimate
was obtained from a single image!
Number of galaxies in the Universe: ____________ galaxies!
Part 3: The Fate of the Universe
Now that we have an estimate for the number of galaxies in the Universe, it’s time to
estimate the mass density of the Universe (The amount of mass divided by the volume). This
number is of vital importance; this single number can tell you the eventual fate of the entire
Universe!
1.) The Milky Way Galaxy is a fairly typical galaxy, neither noticeably bigger nor noticeably
smaller than most other galaxies. We can therefore assume that its mass of 3*1045 g is
the average mass of a galaxy in the Universe. Using this value and your estimate for the
number of galaxies in the Universe, determine an estimate for the total mass of the
Universe.
Total mass of the Universe: _______________ grams.
2.) We now need an estimate for the volume of the Universe that we can see. If we assume
that the farthest galaxy we’ve been able to see, at 13 billion light-years away, is at the
edge of the (observable) Universe, then the radius of the Universe is also 13 billion light4
years, which in centimeters is 1.235*1028 cm. Since the volume of a sphere is 𝑉 = 3 𝜋𝑟 3 ,
what is the volume of the Universe in cm^3?
Volume of the Universe: _______________ cm^3.
3.) The mass density can be found by taking the total mass and dividing by the total
volume. What, then is the mass density of the Universe?
Mass density of the Universe: ______________ g/cm^3.
4.) Gravity extends to the outer reaches of the Universe. Because all the galaxies in the
Universe attract all the other galaxies in the Universe it is possible that the gravitational
pull of all the galaxies will eventually reverse the Hubble expansion. If this happens the
galaxies will begin to fall back together and will lead to a “Big Crunch”. Astronomers
estimate this will happen if the mass density of the Universe is 10-29 g/cm^3. This is
known as the critical density. Compare the value you obtained for the mass density of
the universe with the critical density. If your estimate is correct what is the fate of the
Universe?
Part 4: Additional Questions
1.) During the course of this calculation, we made several assumptions. Each assumption
we make impacts the accuracy of our result. List as many such assumptions as you can,
and comment on a.) Whether you think this assumption was reasonable and b.) How
much you think this affected our result. You should find at least 3 such assumptions!
2.) Based on your answer to question 1 above, do you think your answer for the fate of the
Universe is still reasonable?
3.) Suppose astronomers discovered large clumps of dark matter outside of galaxies, and
spread throughout the Universe. Would this dark matter have been included in our
estimate for the mass of the Universe? What effect, if any, would this discovery have on
our estimate for the mass density of the Universe?