Transcript What is the Minimum Mass Necessary to make a Celestial

Julieanna Bacon
About Me
How many people can say their first word was a celestial object? Probably
not a lot, and when your first word is
Me, on the left, at a DECA
something
like star,
chances are you have already been
leadership
conference
hooked by astronomy. Since that day
about 15 years ago, I have found out that
I won’t be happy doing anything else
but astrophysics. I am now in the 10th
grade at Cooper City High School,
taking Spanish 3
here at FLVS. This is my first course at
the school & the freedom it grants is
extremely gratifying. I have attended
the SPLASH program at MIT, completed college-level astronomy
courses, completed biology and chemistry courses at my high school,
and have served as treasurer for the Science Club at Cooper City High
School. I was elected president for the upcoming 2012-2013 school year
as well. Science has been my passion for as long as I can remember.
Project Introduction
The purpose of this study was to find the minimum required mass for
gravity to make an object spherical. The experiment’s goal was to find a
variety of masses for celestial bodies (both spherical & non-spherical)
using data from various sources & calculate the masses. After much
initial research, 0.0006% of Earth’s mass was hypothesized to be the
critical minimum mass. First a telescope was used that was capable of
measuring the length of time an object takes to orbit another object.
Second, the distance between the two objects was recorded. Next,
Kepler’s 3rd Law was used to simply Newton’s law of universal
gravitation, and using that allowed the final mass of each celestial
object to be calculated. Images from Hubble, Cassini, and other
spacecrafts photographing the solar system were used to determine
curvature, as well as descriptions in scientific publications.
Astronomers and physicists struggle with determining characteristics
of exosolar planets, often only knowing the mass and orbit of the
celestial object. They could apply the minimum mass found here to
determine if the body is spherical or not large enough to attain a
spherical shape. The subjects of the experiment were the 7 celestial
bodies whose mass was tested.
Hypothesis
 The hypothesis was that 0.0006% of Earth’s mass is the
minimum mass required to shape the object into a
sphere by gravity.
 The exact figure predicted was 3.58452 * 10²°
Initial Research and Works Cited
As you know, Pluto was stripped of its status of planet & given the title
“Dwarf Planet”, at the IAU meeting of 2006, which created a new
classification of objects big enough to be round, yet too small to have
cleared their orbit of stray asteroids. When I first heard of this major
event, I was intrigued by this. It inspired me to inquire further. This
new classification also helped narrow down the objects that were to be
subjected to the experiment. The objects being tested had to have a
variety of masses, but none too great otherwise it would not help to
know their masses. The reason the planets in our solar system were not
tested & used to determine the minimum mass, rather than the
hypothesis, was because they are so much bigger than the minimum
mass. Researching various dwarf planets helped find bodies on the
cusp of being round or not round, which were the ones perfect to test.
The 5 IAU recognized dwarf planets are Ceres, Eris, Makemake,
Haumea, & Pluto. Once these dwarf planets were research, it was found
that Ceres is the smallest, but still clearly round.
Initial Research and Works Cited
The implications of this study are many in number. If this study
has not been done before, then imagine knowing the exact figure
that determines if a celestial body is round or not. This would be
most useful to astronomer & astrophysicists. Unless the body
was in a special circumstance, you could know if a body in space
was round or not, simply by knowing it’s mass! This could mean
a great deal of time saved, because previously telescopes had to
be booked many months earlier to check whether or not a body
in space was round, if you were classifying asteroids, moons, or
comets in the solar system. Instead, this could mean that
astronomers no longer need to waste time & money booking
expensive telescopes to simply check if an object was round.
They can book telescopes for more important things now! For
example, measuring the mass & rotation speed of neighboring
galaxies to see how much dark matter they contain & furthering
the study of this mystery.
Initial Research and Works Cited
When studying exosolar planets, astrophysicists, studying
only the tiny “wobble” effect the planet has its sun, can
determine the mass of the planet. Since they are much too
far away to be seen with a telescope, characteristics of the
planet must be deduced. The minimum mass figure can
indicate whether or not the planet is spherical. As
technology improves, astrophysicists will be able to detect
exosolar planets much farther than the 3,000 light years
they have currently reached. As this occurs, they will be
looking farther and farther into the past. Astronomers that
study the early formation of solar systems will find this
data especially useful in determining the history of a
celestial object.
Materials
 Telescope (Celestron – 8”)
 Calculator (Ti-89)
 Paper
 Pencil
 Computer
 Chart
 Newton’s law of universal gravitation, simplified by
Kepler’s 3rd law of planetary motion - M=4 pi2*r3/T2G
Materials
Ti- 89 used in calculations
Celestron NexStar 8 inch Telescope
Method
 There are two basic ways to detect a natural satellite’s mass: the
effect the satellite has on other satellites’ orbits and if the body
has a satellite itself. Newton’s law of universal gravitation can
then be used to determine the mass of the object.
 The independent variables of the experiment were amount of
distance between object A (the object whose mass is being
measured) and object B, and amount of time it takes object B to
orbit object A. The independent variables of this experiment
were chosen as such, because they are the ones that can be
changed to come to a definite mass. They control the experiment
part of this study. The formula used to find the mass of an object
using another object orbiting it is M=4 pi2*r3/T2G (Tom Young
2001) ( see procedures #4 to see what each variable in the
equation stands for).
Method
 The dependent variable in this experiment is the mass
of the celestial body, or simply, the outcome of the
equation after you have done your math & found your
figures via telescope.
 The control of this experiment was the masses of the
celestial objects that can be found online. After the
experiment, the masses found were compared online
with the masses found. The masses found had a large
propagated error, since equipment usually used to find
the masses of celestial objects are telescopes of over 15”.
Procedures
1.
2.
3.
4.
5.
To find the mass of an object such as Pluto (dwarf planet with
moons), you must first find a telescope capable of measuring the
length of time that an object far into space takes to orbit another
celestial object, such as Pluto & Pluto’s moon.
Once you have done that, record the amount of time it takes the
moon (let’s call it object B) to orbit the body (Pluto in this case,
object A).
Find the distance between object A & object B (astronomical records
are the best resources).
Take the equation M=4 pi2*r3/T2G, M being the mass of the orbited
object, T the amount of time it takes the orbiting object to orbit the
planet or sun you want the mass of, pi is 3.14159, R is the distance
between the centers of Objects A&B in meters, and G is the
gravitational constant (6.672 x 10-11 Nm2/kg2).
Plug the numbers in & solve for the mass of object A.
Results
 The final result of the project showed that an object
with a diameter of 400km, give or take 10km, has just
barely enough mass to be spherical. Its mass should be
roughly 1.3 * 10⁸kg. The table below shows the data
collected in this experiment. 9 Metis was included in
the table because since it is close to being spherical,
but not really so, it shows almost the minimum mass
require for gravity to shape a celestial object into a
sphere. The minimum mass is very close to 9 Metis’s
mass. In fact, 10 Hygiea just qualifies as “spherical”,
meaning from any point in its center, the surface is the
same distance within 20km.
Data
Object
Pluto
Mass (kilograms) Moon
1.3 *1022
3
Classification
Dwarf planet
Haumea
4.1 * 1021
2
Dwarf planet
Makemake
4.341 * 1021
Dwarf planet
Eris
1.1*10²²
0 (even though it needs a moon to be
calculated my way, the mass was found
online)
1
Ceres
9.43 * 1020
Dwarf planet
10 Hygiea
1 * 10⁸
0 (even though it needs a moon to be
calculated my way, the mass was found
online)
1 satellite
9 Metis
1.13 * 10⁷
0 (even though it needs a moon to be
calculated my way, the mass was found
online)
Asteroid
(NONSPHEREICAL)
Dwarf planet
Asteroid
Object
Mass Found
Mass Online
Pluto
1 *1022
1.3 *1022
Haumea
4 * 1021
4.1 * 1021
Makemake
n/a
4.341 * 1021
Eris
1 * 10²²
1.1* 10²²
Ceres
n/a
9.43 * 1020
10 Hygiea
1 * 10⁸
1.3 * 10⁸
Conclusion
The hypothesis was that 3.58452 * 10²° is the minimum
mass requires for gravity to shape the object into a
sphere, or 0.0006 of Earth’s mass. The actually
minimum mass turned out to be 1.3 * 10⁸.
The data showed that while 9 Metis was just on the cusp
of being round with a mass of 1.13 * 10⁷, it was 10
Hygiea that just qualified as being round with a mass
of 1.3 * 10⁸kg. The results for this research are versatile.
Conclusion
The implications of this study were mentioned earlier in the
introduction, but to summarize, the conclusion of this
study would most help astronomers & people who study
space. They could save time that is normally used to check
whether an asteroid, moon, comet, etc is round by a very
expensive telescope by simply using the minimum mass to
determine if it is round. So, if the IAU needs to find out if a
large asteroid qualifies as a dwarf planet, they simply need
to know the mass of the object to find out if it is round. If
the mass of the object is above the minimum, then it is
round, unless it is very young or in a special circumstance &
if it is below the minimum, it is not round. This method
can save time & money, both of which can instead be used
for more important things.
Conclusion
After comparing the controls & the data that was found
in the experiment, conclusions were drawn about what
the minimum mass was. Since 10 Hygiea was just
barely round (meeting the requirements as being
“round” by just a smidgeon) its mass seemed the
perfect minimum mass requirement. With 9 Metis
trailing so closely behind, only 1 zero smaller, and yet
definitely not meeting the “round” requirements, it
proved that the remarkable 10 Hygiea was the
minimum, almost exactly.
Discussion
Some limitations of this study might have been that
what qualified an object as being round was not clear
enough or was hard to determine. The minimum mass
may vary from what was deduced. Also, my way of
finding the masses of the celestial bodies was limited
by my resources. Perhaps if a professional telescope
was used, it may have wielded different and more
accurate results. But since controls, the actual masses
of the objects found online from studies done by
NASA and other astronomical organizations, were
used, most error was eliminated from that limitation.
Discussion
A question raised by this study was, is it possible to
determine using this data if an exosolar planet
thousands of light-years away is round? Currently
technology is still too crude to find any exosolar
planets smaller than Earth, so they are all round for
sure, but in 10 years or so from now, when the objects
are so small we have doubts about whether they
qualify as exosolar planets or just exosolar asteroids or
dwarf planets or whatever it may be, will this data help
determine if they are?
12 Candidates for Planets, credit (IAU/NASA) Martin Kornmesser
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