annotated-Project%201-%20How%20Massive%20is%20this%20New%20Planet%3F%20.docx

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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] 37350 X1000 37350000m  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] 15.774 378.576 22714.56 1362873.6 1362873.6 Now we are ready to calculate the mass of the system 4  2 x a 3 /G /P 2 = (m1+m2) 39.4784176 5.210409038 x10 22 6.67384 x10 -11 m 3 kg -1 s -2 1.85742445 X10 12 1.659375244 X10 22 kg

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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. Eris is more massive than Pluto because Pluto’s mass is only 0.01303 x10 24 and Eris’ mass is 1.659375244 X10 22 making Eris’ mass about 1.27 times more than Pluto’s. 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 1.659375244 X10 22 3.14 1200000 2210.49kg/m 3 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? I would expect the composition of Eris to be mostly rocks because it’s density lies within the rocks density range, but I would expect it contain some ices and metals too just like Pluto does.

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. I would have reclassified Pluto as a dwarf planet because it fits well under that classification. Dwarf planets and regular planets are very similar in some aspects such as they both orbit the sun and have round shapes because of their own gravity, but the main difference between the two is that dwarf planets have not cleared the area around their orbit while planets have. Planets are also much larger than 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=22 56