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Comprehension Check Set Newton’s Law of Universal Gravitation equal to the centripetal force and determine the orbital speed of the following planets (mean orbital radius given) if the mass of the sun is 1.991x1030kg): Mecury (5.79x1010m) Venus (1.08x1011m) Mars (2.28x1011m) Neptune (4.50x1012m) Comprehension Check Mercury – 4.79x104m/s Venus – 3.51x104m/s Mars – 2.41x104m/s Neptune – 5.43x103m/s Orbital Speed vs Orbital Radius Orbital Speed (m/s) 60000 50000 40000 30000 20000 10000 0 0.00E+0 1.00E+1 2.00E+1 3.00E+1 4.00E+1 5.00E+1 0 2 2 2 2 2 Orbital Radius (m) Dark Matter Physics 12 Video Questions 1. 2. 3. How would you describe the graph that best shows the v against r relationship for planets orbiting the Sun? How would you describe the graph that best shows the v against r relationship observed for stars orbiting the centre of a galaxy? When astronomers measure the mass of the galaxy Triangulum using the Brightness Method the result they get is much less than when they measure the mass using the Orbital Method. This fact can best be explained by the fact that: the stars in Triangulum are made of lighter elements than those in the Sun. the Orbital Method underestimates the mass of Triangulum. Triangulum contains a large amount of unseen mass. Triangulum contains only mass that emits visible light. 4. Observations that indicate the presence of dark matter have been made in: 5. Evidence for dark matter comes from observations of: 6. the orbit of the Moon around Earth and gravitational lensing. the orbits of stars and gravitational lensing. the orbit of the Moon around Earth and the orbits of stars. the orbits of stars, the orbit of the Moon around Earth, and gravitational lensing. Dark matter is called “dark” because it: 7. only the Andromeda and Triangulum galaxies. only the Andromeda, Triangulum, and Milky Way galaxies. every galaxy that has been examined for dark matter. many, but not all, galaxies that have been examined for dark matter. only emits high-energy radiation such as X-rays and gamma rays. only emits low-energy radiation such as microwaves and radio waves. reflects light but does not emit other radiation like stars do. does not emit or reflect any type of radiation or light. Most physicists think that most dark matter is made of: WIMPs or axions. brown dwarf stars. black holes or planets. stars like the Sun. Astronomers have studied galaxy UGC 128 for many years. They have measured its brightness and calculated that the mass of stars within a radius of 1.30 x 1021 m is 3.34 x 1040 kg. Stars orbiting at this radius has been measured travelling at a speed of 1.30 x 105 m/s. What percentage of the mass within this radius is dark matter? Orbital radius of star (x 1020m) Measured speed (x 105 m/s) Calculated speed (x 105 m/s) Gravitational Mass (x1041 kg) Missing Mass (%) 1.85 2.47 2.36 1.69 8.99 2.75 2.40 3.18 2.37 4.26 2.25 6.48 2.47 1. Use the values from the table above to plot measured speed against orbital radius on the graph provided. Label this line “measured”. 2. For each orbital radius, calculate the speed expected if the only mass is the luminous mass of 1.54 x 1041 kg. Record your answers in the “Calculated speed” column. 3. Plot calculated speed against orbital radius on the graph provided. Label the line “calculated”.