on Collider (LHC) is a circular particle accelerator with a circumferen n fast-moving protons collide head-on with other fast-moving protor goals was to detect the Higgs boson, the last undiscovered partici- fundamental particles: the Standard Model. In this activit the laws of conservation of momentum and ener Part 1: Modelling the C The LHC accelerates of the speed ~ circula* The Mystery of Dark Matter Activity 4 NAME : Mohammed Dial Dark Matter Within a Galaxy Al sharaa Useful formulas Fro = ma F - my Fo = GMm G=6.67 x10-"Nm/kg2 Orbital radius Measured Calculated Gravitational mass Missing of star speed speed (x 1020 m) (x 105 m/s) (x 105 m/s) (x 1041 kg) Mass ( % ) 1.85 2.47 2.36 1.69 8.99 2.75 2.40 2 3 3.18 2.37 18 2 . 6 4.26 2.25 1 55 3 , 2 6.48 2.47 1 26 5 . 9 Astronomers have analysed the stars in the galaxy UGC 11748. They found that most of the stars lie within a radius r = 1.64 x 1020 m and that the total mass within this radius is 1.54 x 104 kg, or 77.4 billion times the mass of the Sun. It is expected that the stars that lie outside this radius will orbit in the same way that planets orbit the Sun. In this activity you will analyse the motion of stars located in the outer regions of UGC 11748. . Use the values from the table above to plot measured speed against orbital radius on the graph provided. Label this line "measured". 2.00 2. a) For each orbital radius, calculate the speed expected if the only mass is the luminous mass of 1.54 x 104 kg. Record your answers in the "Calculated speed" column. Speed (x 105 m/s) b) Show a sample calculation. 1.0 c) Plot calculated speed against orbital radius on the graph provided. Label the line "calculated". 2 3 the sured Orbital Radius (x1020 m) calculated 3. Compare the "measured" and "calculated" plots. Discuss a possible explanation for any differences. keeping the march ofe's tars constant be/ calcut ating that they could by liguepage for smallerstars PERIMETER PI INSTITUTE FOR THEORETICAL PHYSICSice of 27 km. the Collision tons. One of the LHC's ticle in scientists' current model of ccelerates protons to over 99.99% speed of light. Different protons Vity, you will use real data from the LHC and energy to determine the mass of the Higgs boson. in opposite directions so they can ad-on. When two protons collide, s can happen. The outcome that ested in is the production of a Position article called the Hiane son quickly- The Mystery of Dark Matter 4. a) Use the measured speeds to calculate the mass of the galaxy contained within each orbital radius. Record your answers in the "Gravitational mass" column. b) Show a sample calculation. FC = MV 2 r F = GM M m = . GM 5. For each orbital radius, calculate the difference between the gravitational mass within this radius and the total mass of the visible stars (1.54 x 1041 kg). Represent this difference as a percentage of the gravitational mass within the orbital radius. Record your answers in the "Missing Mass" column. 6. Do your results support the following statement? "It is reasonable to expect that stars orbit around the gravitational mass contained within the radius of their orbit in the same way that planets orbit around the Sun." Discuss. 7. Explain the shape of your plot for measured speed against orbital radius. Activity 4 | 19 PERIMETER INSTITUTE FOR THEORETICAL PHYSICS