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Lab #10: Star Motion in the Milky Way Objectives: e Understand how stars move in the Milky Way Galaxy e Get a big picture view of the Milky Way Galaxy e Compare star motion with planet motion and the concept of enclosed mass e Think some more about mass and gravity Name: Lab partner(s): Date: Most Things Spin * Most things in the universe rotate: the earth spins around its axis, the planets orbit around the sun, and the sun moves around the center of the Galaxy. We also know from Kepler and Newton that how fast objects orbit is related to the gravity that they feel, which comes from the enclosed mass of the object(s) they are orbiting. B Enclosed mass is how much mass g you'd find inside the orbit of the thing Enclosed _ '3(:, .\\' + o 4 ' 4 @ you're considering. To calculate it, Mass - W you need to add up the masses of all ~ For Mars objects closer to the center, including the sun! For example, Mars. Mars is located on the outside of the red circle in the solar system diagram below. The 11 fill this out _fo Venus (bElOW) b enclosed mass for Mars, the mass Aty around which Mars is orbiting, Enclosed __ '}@! '3'.. E would be M_sun + M_mercury + Mass ALY ? M_venus + M_earth For Venus D Or Venus. Venus orbits the mass enclosed in the green circle below. What would its enclosed mass be? Fill out the diagram to the right like the one for Mars above, but for Venus' situation Part 1: Motion of planets in our solar system * This is a plot of the enclosed mass for each planet in our solar system: /-'r-o-oa-- &9 Enclosed Mass (#x Mass_sun) Value at the location of each planet o * As you can see, the amount of mass that each planet orbits around is approximately the same no matter how far away it is from the sun. Any way you round it, 1.001 is still basically 1 * We know there are asteroids, moons, planets, and space debris (like meteoroids) between each planet and the sun. But all that mass is so tiny compared to the sun that it barely counts at all. * The mass that each planet rotates around is the same. The mass controlling the rotation of the solar system is 1.0 x the Mass of the Sun. Part 1: Motion of planets in our solar system * Make a plot of the orbital speed of each PLANET as a function of distance from the sun. * Plot or Graph, by drawing or on a tablet (but NOT with Excel) Mercury 50 km/s Venus 35 km/s 0.7 1.00000015 Earth 30 km/s 1 1.00000265 Mars 25 km/s 1.5 1.00000565 Jupiter 15 km/s L) 1.00000595 Saturn 10 km/s 10 1.00100595 Uranus 6 km/s 19 1.00125595 Neptune 5km/s 30 1.00129960 ) == = Q Q o wh S BR s BR o g Value at the location of each planet Q2: Using your orbital speed plot above, answer the question: How does the orbital speed change compared to the enclosed mass, as a function of distance? (example: When the mass enclosed the orbital speed of objects orbiting that mass with increasing distance from the center) Part 2: Motion of stars in our galaxy * Do stars in the galaxy move like planets in our solar system? Maybe! Let's look at the data! Ring Stellar Mass Rotation | speed 1 5 billion suns 260 km/s 2 | 20bilionsuns | 210 km/s 3 15 billion suns 240 km/s 4 | 10bilionsuns | 220 km/s X (the sun) 5 1 billion suns 240 km/s * We divide our galaxy into 5 different rings to make it easier to think about * Rotation speed is the same thing as orbital speed, but is an average for all the stars and gas and dust in the given ring (instead of an average speed for one planet) * The enclosed mass of Ring 4 will be the sum of all the material within the orbit of Ring 4, but unlike our planets, this also INCLUDES Ring 4 itself: Enclosed mass = Ring 1 4 Ring 24 Ring 3 4 Ring 4 for Ring 4 Part 2: Motion of stars in our galaxy * Make a plot of the mass in our Milky Way as a function of distance from the nucleus: 50 (# x billions of _sun) w b o o Enclosed Mass Mass sun = M oo o 1 2 3 4 5 Distance Interms of Ring number * As you can see, the amount of mass increases as we move further and further away from the galactic center * This is because there is a significant amount of mass in the gas, dust, and stars of the galactic plane * Plot your estimate. At distances bigger than about 50 kly (beyond Ring 5) from the nucleus, we can assume that there is zero (0) mass to include. Estimate what this means about enclosed mass and add rings 6, 7, 8, and 9 to the Enclosed mass plot you have made above Q3: What is the equation for Enclosed Mass for Ring 8 (similar to the example on the previous page)? Part 2: Motion of stars in our galaxy * Make a plot of the rotation speed of each ring as a function of distance from the center of the galaxy. * Plot or Graph, by drawing or on a tablet (but NOT with Excel) 260 240 Rotation speed 5 Dista nce In terms of Ring number * Assume that there are NO stars beyond Ring 5. Draw your prediction for what the rotation speed would be for anything found in rings 6, 7, 8, and 9. * Add this to the plot above * Clearly indicate that the line or points you are using are for your prediction (use a different color or symbol) * Base this off of what we see in our own solar system, when the enclosed mass becomes a constant value Part 2: Motion of stars in our galaxy Now let's see how this prediction matches up with the data! Based on the motions of clouds of hydrogen gas that surround the galaxy. Ring Stellar Mass Rotation speed 6 0 suns 270 km/s T 0 suns | 280 km/s 8 0 suns . 200 km/s 9 0 suns 300 km/s * Make a plot (final plot) of the rotation speed of all 9 rings of the galaxy * Include appropriate range of numbers on the Y-axis (km/s) Rotation Speed 1 2 3 4 5 6 7 8 9 Distance Intermsof Ring number Q4: Does this match your prediction on the previous graph? Why or why not? Part 3: Consider the graphs and data 1. Describe precisely the behavior of the data in the Part1 orbital speed graph by answering ONE of the following parts, A or B: A. Inour solar system, how does the orbital speed of a planet change as its distance from the sun increases? B. In our solar system, how does the orbital speed of a planet change as it gets closer to the sun? 2. Describe precisely the behavior of the data in the Part2 rotation speed graph (the final one, with all 9 rings included) by answering ONE of the following parts, A or B: A. How does the rotation speed of our galaxy change as its distance from the galactic center increases? B. In our galaxy, how would the rotation speed of an average star change if we looked closer to the galactic center? 3. What does the final plot (that includes all 9 rings worth of data) tell us about the total enclosed mass at these distances? How can we explain this