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Project #1: How Massive Is This New Planet?
On July 29, 2005, astronomers Mike Brown (Caltech), Chad Trujillo (Gemini
Observatory), and David Rabinowitz (Yale) announced the discovery of the tenth
planet in our solar system. This was the first time an object that big had been found
in our solar system since the discovery of Neptune’s moon Triton in 1846. In a
lecture given at NASA’s Jet Propulsion Laboratory, Brown talked about the discovery
and how they came to the realization that it was a planet. "Every time you find indications of an object in the outer solar system, you get a
little charge. You go through all this data, and there's nothing there, nothing there,
nothing there, and then suddenly there's something that no one has ever seen
before except for you. It's always a moment of excitement. Every once in a while, the
moments of excitement almost make you fall out of your chair.
One day we found something that was moving really slow, slower by a factor of two
than anything that we'd seen before, which tells you it's essentially a factor of two
further away. That's enough to make you fall out of your seat to begin with, because
we'd found almost nothing at that distance in the solar system. We first named our
discovery 2003 UB313. That's kind of a dumb name, so we nicknamed it Xena. But
now the official name for this object is Eris.
There are a couple of things you want to learn very quickly when you find one of
these things. One of them is, what does its orbit look like? Is it going to fit the
circular pattern of planets, or is it going to fit Pluto's crazy pattern? It turns out this
one has a 560-year orbit. To track its orbit you have to look over a relatively
significant chunk of its orbit. Three hours is not significant, but we have no patience
for tracking it over a long time.
This object was so bright it was easy to find it in everybody else's old data. Many
people had seen it before but they were doing some other type of project, taking a
picture for other purposes. We found it in photos dating all the way back to 1950.
…
It turns out that its orbit is even crazier and more elongated than Pluto's. Pluto is
tilted by 19 degrees compared to the discs of the other planets. Eris is tilted by 45
degrees. Nobody has a good explanation for why that is.
…
One thing everybody wants to know is how big Eris is. When we see planets,
asteroids, or other nearby bright objects in the sky, what we're seeing is sunlight
reflected from the surface of that object. You can get a lot of sunlight reflected in two
ways: you can either have a relatively small object with a very shiny surface, a snow-
or ice-covered surface, that will reflect a lot of sunlight, or you can have a really big
object with a darker surface. Either way, you get the same amount of sunlight
reflected back, and you can't tell which it is just by looking at it.
So astronomers have come up with these very clever techniques, using images from
things like the Spitzer Space Telescope, to figure out how much heat is coming from
the object, and that could indicate how big it is. We're less clever than most
astronomers, so we decided to take pictures with the Hubble Space Telescope.
Usually you can't do that, because the objects are so small they just look like a point
of light even with Hubble. But as bright as it was, it had to be bigger than Pluto, so
we knew we would be able to see it with Hubble and measure precisely how big it
was.
The size (diameter) is 2400 kilometers or 2,400,000 meters, with an uncertainty of
about 100 kilometers. Pluto is about 2370 kilometers, depending on whom you ask.
So this thing is just barely bigger than Pluto. Finding the largest dwarf planet is not
quite as exciting as finding the tenth planet, but I'd just like to point out that Eris is
the largest dwarf planet in the known universe."
ERIS AND ITS MOON
The Hubble images of Eris show that the new dwarf planet is slightly larger than
Pluto, but the mass of the planet could only be calculated by observing the orbital
motion
of
its
moon
Dysnomia. Multiple images of
the moon were taken by
Hubble Space Telescope and
W. M. Keck Observatory to
precisely measure the new
planet’s mass. We will use
these observations and what
we know about gravity to
estimate the mass of Eris, its
density and composition.
Question 1 (30 points)
In class this week, you learned about Newton’s version of Kepler’s third law. This equation uses the period, P
, of an orbit (how long an object takes to complete one orbit around another) and the average distance, a
, between the two objects to estimate the mass of a system, (m1 + m2)
. In astronomy we use this equation to calculate masses of planets, stars, and even galaxies or black holes. Let’s find out if Eris is really more deserving of being called a planet than Pluto by calculating the mass of Eris and comparing our result to the mass of Pluto. Newton’s equation is:
Equation (1):
From the observations of Dysnomia, Mike Brown and his team were able to see that Dysnomia has an almost-circular orbit with an average distance, a
, to Eris of 37,350 km and an orbital period, P
, of 15.774 days. Using these orbital parameters, what would the combined mass of the system be?
You will need:
= 3.1415
G (gravitational constant) = 6.67384 × 10
-11
m
3
kg
-1
s
-2
Watch your units!
The gravitational constant, G
, is given in meters, m, and the average distance,
a
, in km. You will need to change the average distance to meters before you use it in the equation.
a [km]
x 1000 [m/km]
= a [m]
37,350
x 1000[m/km]
37,350,000
The gravitational constant, G
, also has units of seconds, s, and the period of Dysnomia is given in days. You will need to change the period to seconds before you use it in the equation.
P [days]
x 24 [hr/day]
x 60 [min/hr]
x 60 [s/min]
= P [s]
15.744
x 24 [hr/day]
x 60 [min/hr]
x 60 [s/min]
1,362,873.6 s
Now we are ready to calculate the mass of the system
4
2
x a
3
/G
/P
2
= (m1+m2)
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4
2
3.725*10
7
1/6.67384*10
11
1/1362873.6
1.6461*10
22
This mass that you just calculated is the combined mass of Eris and Dysnomia; however, the mass of Dysnomia is very small relative to the mass of Eris and can be neglected. Therefore, the mass you obtained is essentially the mass of the planet. Question 2.
(10 points) Look up the mass of Pluto in NASA’s Pluto Fact Sheet
. http://nssdc.gsfc.nasa.gov/planetary/factsheet/plutofact.html
. Is Eris more or less massive than Pluto? Explain.
The mass of Pluto is 1.303*10
22
. That mass is less than the one calculated to be Eris, 1.6461*10
22
. Eris has more mass because of the mass of Dysomina that’s really small. Question 3.
(20 points) Now that you have calculated the mass of this newly discovered planet, you can also calculate its density to see what is made of. The density of an object can be calculated by dividing the mass of the object by the volume. We will assume Eris is a sphere and use the volume of a sphere for this step.
In the introduction to his assignment, Mike Brown gave the size of the planet that his team obtained from the Hubble images. This is the diameter of the planet so you need to divide this by two to get the radius. Equation (2): Density = Mass/Volume
Watch your units!
Equation (3): Volume of a Sphere = 3/4 x mass [kg]
/
/radius [m]
3
= density [kg/m
3
]
3/4
1.6461*10
22
1/
1/2400000/2
2274.17 kg/m3
Question 4.
(20 points) Compare the estimated density that you obtained above with the density of water (1,000 kg/m
3
), Rocks (2,000 to 4,000 kg/m
3
), and Iron (7,800 kg/m
3
). Do you expect the composition of Eris to be mostly ices, rocks, or metals? Why? Density of 2274.17 kg/mg3 because of the composure of rocks.
Question 5
. (20 points) Based on what you have learned about Eris and Pluto, would
you have reclassified Pluto as a dwarf planet? Explain. What are the properties or a dwarf planet? What are the properties of a regular planet? You can use what you have learned on this project on your Discussion Forum for Module 2. A planet is defined as one that orbits the sun on its own, has enough mass that gravity draws it into a spheroidal form, and has the capacity to either take control of
its orbit or cause objects to be drawn into it by its gravitational pull. Due to its little mass, Pluto is unable to attract anything into its orbit. Since Neptune is 8,000 times larger than Pluto, for instance, I would reclassify Pluto as a dwarf planet because, if any planet differs from the others in some way, such as having a weak gravitational pull, it shouldn't be included in the group of planets that fall under the same category as dwarf planets.
References:
Science 15 June 2007, Vol. 316 no. 5831 p. 1585 http://www.astrobio.net/index.php?
option=com_retrospection&task=detail&id=2256