gravity_force_lab (1)

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Physics

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Apr 3, 2024

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docx

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Gravity Force Lab Worksheet Name: Cheyenne Rahman Purpose In this experiment, you will explore the relationships between gravity and the motion of orbiting bodies. Important formulas and constants: Speed of Circular Orbit Orbital Period Period of Circular Orbit Around Object Constants v = √ GM r T = 2 πr v T 2 = ( 4 π 2 GM ) r 3 1 AU = 1.5 × 10 11 m 1 year = 31,557,600 s 1 kilometer = 1,000 m G = 6.67 × 10 –11 N·m 2 /kg 2 Pre-Lab Questions 1. Explain why the mass of a satellite is not part of the formula for calculating its circular orbital speed? - Because of the mass of the satellite, it excludes the other components in the calculations and the mass of the earth is influenced by gravity while the satellite isn’t. In Newton’s 2 nd law, it only requires the radius of the orbital speed and mass of larger objects. 2. Earth is 1 AU from the sun, on average due to its almost circular orbit. The sun has a mass of 1.9891 ×10 30 kg. a. Calculate the speed of Earth Show your work. b. Calculate the orbital period of Earth. Show your work. c. Does your answer in part b match the number of seconds in a year? Explain why or why not? Unless Otherwise Noted All Content © 2023 Florida Virtual School. FlexPoint Education Cloud™ is a trademark of Florida Virtual School.
Exploratory Component Select the Lab tab. You will see two bodies. The larger mass is the star, and the smaller mass is the satellite. For this lab, you will have these default settings : Select the check boxes for More Data, Path, Velocity, and Values. Ensure the velocity of the large object is 0 km/s. You can do this by inputting 0 in the V x and V y top boxes. For the mass of the small object, input 0.1. Ensure the position x (distance) of the small object is 2.0 AU, position y is 0.0, V x = 0, and V y = 21.1 km/s. 1. Run the simulation. Describe the satellite's orbital motion (shape of path and changes to velocity) and record the time to complete one revolution (period) in the data table. 2. Press the restart button. This is the |< < button at the top, not the reset button at the bottom right. If you accidentally pressed reset, redo to default settings again. 3. Change the mass of the star to 100.0. Run the simulation and record your observations. 4. Restart and change mass of star to 300. Run the simulation and record your observations. Remember to change the mass of the small object to input 0.1 Unless Otherwise Noted All Content © 2023 Florida Virtual School. FlexPoint Education Cloud™ is a trademark of Florida Virtual School.
5. Restart. Complete the remaining trials based on the parameters. The bolded red values show the initial conditions that change. Note: zoom out to see larger orbits or change simulation's speed to Fast for longer periods. Ma ss of Sta r, M (10 2 8 kg) Dista nce of Satelli te, x (AU) Veloci ty of Satelli te, v (km/s ) Observation of orbital motion Peri od, T (yea rs) 200 .0 2.0 21.1 2.9 100 .0 2.0 21.1 1.5 Unless Otherwise Noted All Content © 2023 Florida Virtual School. FlexPoint Education Cloud™ is a trademark of Florida Virtual School.
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300 .0 2.0 21.1 1.6 200 .0 1.0 21.1 0.5 Unless Otherwise Noted All Content © 2023 Florida Virtual School. FlexPoint Education Cloud™ is a trademark of Florida Virtual School.
200 .0 3.0 21.1 14.9 200 .0 2.0 10.0 1.3 Unless Otherwise Noted All Content © 2023 Florida Virtual School. FlexPoint Education Cloud™ is a trademark of Florida Virtual School.
200 .0 2.0 28.0 23.9 The satellite needs to have an orbital speed of 21.1 km/s when it is 2.0 AU from a star with mass 200 × 10 28 kg. Answer the following questions in complete sentences to analyze your observations. 1. Summarize the conditions of a star's mass and distance of a satellite that result in a fast elliptical orbit of a satellite. 2. What objects in space are best modeled by the conditions of the last trial? Justify your answer. 3. The Earth moves around the Sun at velocity v 1 . In a neighboring star system, a satellite is in a circular orbit around a planet of mass M at a velocity of v 2 , and distance of r . If v 2 > v 1 , what characteristics of the neighboring star system can you infer? Briefly explain. Quantitative Component In the exploratory component, you observed how orbits are based on mass, distance, and speed. You will now calculate the exact speed required to maintain circular orbits and verify with the simulation. For example, when the default settings showed a circular orbit. This is confirmed because the velocity values of the satellite are fairly consistent throughout the orbit. Start with the default settings. For each trial, you are given the mass of the star and the distance of the satellite. Unless Otherwise Noted All Content © 2023 Florida Virtual School. FlexPoint Education Cloud™ is a trademark of Florida Virtual School.
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1. Calculate the speed required for a circular orbit. Remember to convert AU to meters. Convert your speed to km/s and record in the table. Show your work. 2. Calculate the period of this orbit. Record in the table. Show your work. 3. Zoom out all the way in the simulation. Input the values for mass, distance, and speed (in V y ). 4. Run the simulation. Did you correctly calculate a circular orbit? If so, copy the orbital period in years. Are the times you calculated and what the simulation gave close enough? 5. When done, take a screenshot the trial (with circular path shown), and include in this lab report. Trial Mass of Star, M (10 28 kg) Distance of Satellite, x (AU) Speed for Circular Orbit, v (km/s) Orbital Period, T (s) Orbital Period, T (years) 1 100.0 2.0 15 km / s 1.26 ∙ 10 8 4.1 2 200.0 1.0 30 km/s 3.14 x 10^7 1.2 3 300.0 2.0 26 km/s 7.25 x 10^7 2.4 4 300.0 4.0 18 km/s 2.09 x 10^8 6.4 You can show work and include screenshots for each trial below. Unless Otherwise Noted All Content © 2023 Florida Virtual School. FlexPoint Education Cloud™ is a trademark of Florida Virtual School.
Unless Otherwise Noted All Content © 2023 Florida Virtual School. FlexPoint Education Cloud™ is a trademark of Florida Virtual School.
Application Component Use your investigation to answer the following questions. You will refer to the tables above. The mass of the satellite is 0.1 × 10 28 kg. 1. Explain why the gravitational force acts as the centripetal force for satellites in orbit. 2. Use data from two of your trials. Calculate the centripetal force F c = mv 2 r acting on the satellite for each trial. Show your work. 3. Use the same trials and calculate the gravitational force between the star and the satellite. Show your work. 4. How do your calculations in questions 2 and 3 compare? Unless Otherwise Noted All Content © 2023 Florida Virtual School. FlexPoint Education Cloud™ is a trademark of Florida Virtual School.
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