Project1_Module2_Eris

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University of Florida *

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AST 2001

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Astronomy

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Feb 20, 2024

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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] 37,350 km 37,350(1000m/ 1km) 37,350,000m  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] 15.77 4 15.774(24hr/ 1day) 378.576(60min/ 1hr) 22,714.560(60s/ 1min) 1,362,873.6 00 s Now we are ready to calculate the mass of the system

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