Lab 07 - WorkSheet-1

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Apr 3, 2024

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ASTR 110L Lab 07 Lab 07 PhET WorkSheet In each Part, follow the Instructions. For each Question (e.g., 1A, 2C, etc.), enter your answers in this doc. Paste in Screenshots (preferred) or jpegs, as required. Give complete and well-thought-out answers. Part 1. Is the orbit of this planet circular? (20 points total) Press the TO SCALE option at the bottom of the screen with the star and planet chosen in Box 1. Press the Reset button. Set the upper left slider to minimal magnification. Select the Path and Grid options. Allow the planet to move through 360 o . Once 360 o has been reached, Pause the motion. The time should read 365 Earth Days. Turn on the Measuring Tape. Along a horizontal grid line, measure the horizontal distance from the Path on the left to the Star. Write this measurement in the box below. Now do the same from the Star to the Path on the right. Write this measurement in the box below. 1A. Distance (km) (10 points total) Left Side: From Path to Star: __152289447____ Right Side: From Path to Starr: __146781680___ 1B. What do you notice about the distances? (5 points total) The left side path to the star is a further distance than the right path to the star. 1C. What does this data say about the orbit of the Planet? Discuss. (5 points total) The planet doesn’t orbit the planet with the planet staying consistently in the middle.

ASTR 110L Lab 07 Part 2. Analyzing an Orbit with Vectors (25 points total) Press the MODEL option at the bottom of the screen. Press the Reset button. Set the upper left slider to minimal magnification. Select Sun and Planet. Select Gravity Force, Velocity, Path, and Grid. Gravity must be turned ON . Press the Play button, let the Planet complete one cycle around the Sun, and then press Pause. Make note of the Orbital Time. Take a screenshot of the full trajectory. (Because of the orbit length, it is possible that it may have begun to self-erase.) The Screenshot will be pasted on the next page. 2A. What holds the Planet in its orbit? (5 points total) The gravity force of the star 2B. What shape is the orbit? Discuss. (5 points total) The shape is a circle. 2C. In what direction do the 2 Gravity Forces face in the Screenshot? What does this imply? (5 points total) The gravitational forces are pulling towards each other

ASTR 110L Lab 07 2D Insert Screenshot 1 here ; adjust its size for easy viewing. Screenshot 1 . (10 points total)

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ASTR 110L Lab 07 Part 3. The Effect of the Absence of Gravity (25 points total) Press the MODEL option at the bottom of the screen. Press the Reset button. Set the upper left slider to minimal magnification. Select Sun and Planet. Select Gravity Force, Velocity, Path, and Grid. Gravity must now be turned OFF . Press the Play button, allow the Planet to move, and then press Pause. Take a screenshot of the trajectory. The Screenshot will be pasted on the next page. 3A. What happens to the Planet in this case? Why? (5 points total) Since there is no gravitational pull present, the planet’s “orbit” went into a straight line upwards 3B. While the Planet is in its current position, grab the tip of the vector and rotate it to some other angular position. Stretch or shrink the vector to some other length. Then press the Play button, allow the Planet to move, and then press Pause. What happens to the Planet in this case? Why? (5 points total) The planet moves in direction of the velocity due to inertia, according to Newton’s first law of motion. 3C. While the Planet is in its new current position, rotate its Velocity vector to point directly at the star. Then press the Play button, allow the Planet to move. What happens to the Planet in this case? Why? (5 points total) The planet orbits into the star and explodes.

ASTR 110L Lab 07 3D. Insert Screenshot 2 here ; adjust its size for easy viewing. Screenshot 2 . (10 points total)

ASTR 110L Lab 07 Part 4. The Effect of a Small Increase in the Starting Velocity (35 points total) Press the MODEL option at the bottom of the screen. Press the Reset button. Set the upper left slider to minimal magnification. Select Sun and Planet. Select Gravity Force, Velocity, Path, and Grid. Gravity must now be turned ON . The Velocity vector should be approximately 1.8 grid-units long . Stretch the Velocity Vector to be about 2.0 grid-units long . Maintain its vertical orientation on the screen so that it points in the same direction. Press the Play button, allow the Planet to move through one orbit, and then press Pause. Make note of the Orbital Time. Take a screenshot of the trajectory. The Screenshot will be pasted on the next page. 4A. How is this orbit different in shape from that in Part 2? Specifically, how does the left Path-Star distance compare to the right Path-Star distance? (5 points total) The star is closer in distance to the right path of the planet’s orbit. 4B. Why does the shape of the orbit change when the starting Velocity is increased? (5 points total) When the starting velocity of a planet is increased, the balance between the gravitational pull towards the sun and the planet’s inertia, leading to orbital change. 4C. The length of the Velocity vector is related to its speed. Describe the length of the Velocity vector as the planet goes around one orbit. Why does this change occur? (5 points total) The circle becomes bigger, traveling further and forming a circle, and a full orbit that takes longer than 365 days. 4D. The Gravity Force depends on the Star’s and the Planet’s masses, which here don’t change. The Gravity Force also depends on the center-to-center distance between the Star and the Planet. Describe the lengths of the Gravity Force vectors as the Planet goes around one orbit. Why does this change occur? (5 points total) With a higher velocity, as planet’s inertia can become strong enough to overcome the gravitational pull. 4E. What is the new orbital time (the period)? How does that compare with the orbital time found in Part 2? (5 points total) 531 earth days, it is 166 more days than part 2.

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ASTR 110L Lab 07 4F. Insert Screenshot 3 here ; adjust its size for easy viewing. Screenshot 3 . (10 points total)

ASTR 110L Lab 07 Part 5. The Effect of a Large Increase in the Starting Velocity (20 points total) Press the MODEL option at the bottom of the screen. Press the Reset button. Set the upper left slider to minimal magnification. Select Sun and Planet. Select Gravity Force, Velocity, Path, and Grid. Gravity must now be turned ON . The Velocity vector should be approximately 1.8 grid-units long . Stretch the Velocity Vector to be about 2.4 grid-units long . Maintain its vertical orientation on the screen so that it points in the same direction. Press the Play button, allow the Planet to move through one orbit, and then press Pause. Make note of the Orbital Time. Take a Screenshot of the trajectory. The Screenshot will be pasted on the next page. 5A. In what ways is this orbit different from that in Part 4? (5 points total) It does not go to form a circular orbit but orbits moving up left. 5B. What are two possible scenarios for this planet? (5 points total) Increased velocity escaped the gravitational pull of the sun. Path changed from an ecliptic path to an open path.

ASTR 110L Lab 07 5C. Insert Screenshot 4 here ; adjust its size for easy viewing. Screenshot 4 . (10 points total)

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ASTR 110L Lab 07 Part 6. The Effect of a Small Decrease in the Starting Velocity (35 points total) Press the MODEL option at the bottom of the screen. Press the Reset button. Set the upper left slider to minimal magnification. Select Sun and Planet. Select Gravity Force, Velocity, Path, and Grid. Gravity must now be turned ON . The Velocity vector should be approximately 1.8 grid-units long . Stretch the Velocity Vector to be about 1.5 grid-units long . Maintain its vertical orientation on the screen so that it points in the same direction. Press the Play button, allow the Planet to move through one orbit, and then press Pause. Make note of the Orbital Time. Take a Screenshot of the trajectory. The Screenshot will be pasted on the next page. 6A. How is this orbit different in shape from those in Parts 2 and 4? Specifically, how does the left Path-Star distance compare to the right Path-Star distance? (5 points total) The orbit creates a smaller circle and the left of the path star distance is shorter than the right path star distance. 6B. Why does the shape of the orbit change when the starting Velocity is decreased? (5 points total) A decrease in velocity means greater gravitational pull. 6C. The length of the Velocity vector is related to its speed. Describe the length of the Velocity vector as the planet goes around one orbit. Why does this change occur? (5 points total) Because of the short length of the velocity vector, the suns gravitational pull is greater resulting in the planet speeding up as it falls closer to it. 6D. The Gravity Force depends on the Star’s and the Planet’s masses, which here don’t change. The Gravity Force also depends on the center-to-center distance between the Star and the Planet. Describe the lengths of the Gravity Force vectors as the Planet goes around one orbit. Why does this change occur? (5 points total) Because of the short length of the velocity, vector, and the speed of the planet orbiting, it creates a smaller circle, and the full orbit is shorter than 365 days. The force between the two objects is directly proportional to the product of their masses, and inversely proportional to the square of the distance between their centers.

ASTR 110L Lab 07 6E. What is the new orbital time (the period)? How does that compare with the orbital times found in Parts 2 and 4? (5 points total) 271 earth days, the shortest of the orbital times recorded. 6F. Insert Screenshot 5 here ; adjust its size for easy viewing. Screenshot 5 . (10 points total)

ASTR 110L Lab 07 Part 7. The Effect of a Large Decrease in the Starting Velocity (25 points total) Press the MODEL option at the bottom of the screen. Press the Reset button. Set the upper left slider to minimal magnification. Select Sun and Planet. Select Gravity Force, Velocity, Path, and Grid. Gravity must now be turned ON . The Velocity vector should be approximately 1.8 grid-units long . Stretch the Velocity Vector to be about 1.0 grid-units long . Maintain its vertical orientation on the screen so that it points in the same direction. Press the Play button, allow the Planet to move through one orbit, and then press Pause. Make note of the Orbital Time. Take a Screenshot of the trajectory. The Screenshot will be pasted on the next page. 7A. In what ways is this orbit different from that in Part 6? (5 points total) The planet orbits into the sun and explodes 7B. Why does the Path change when the starting velocity is sizably decreased? (5 points total) The gravitational force is strong enough to keep the planet in a nearly circular orbit. The planet’s inertia doesn’t overpower the gravitational pull. 7C. What was the total time recorded for this Planet here? (5 points total) 78 days

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ASTR 110L Lab 07 7D. Insert Screenshot 6 here ; adjust its size for easy viewing. . Screenshot 6 . (10 points total)

ASTR 110L Lab 07 Part 8. Experimental Analysis of Satellite Orbital Configurations (35 points total) In this section, we will be constructing three sample orbits with different starting conditions. We will use the Earth/satellite combination. The Satellite, in this case, is in Low Earth Orbit, with the orbit being approximately circular. Using a transparent plastic metric ruler, the altitude from the earth’s surface to the starting point of the satellite is about 2 mm; we’ll call this distance D. Distance measurements here will be easier with a background that is not so dark. In the bottom right of the screen, there is the word PhET, followed by 3 dots. Click on those 3 dots. A window opens with the top line saying “Options . . .”. Click on Options and select Projector Mode. Click the X in the upper right to close the window. The screen is now white. In this Experiment, we will be keeping the Velocity vector the same length and will not be orienting it to any different angles. We will only be sliding the vector to the right and measuring the orbital times at D, 2D, 3D, 4D, and 5D. Press the MODEL option at the bottom of the screen. Press the Reset button. Set the upper left slider to minimal magnification. Select Earth and Satellite. Select Velocity, Path, and Grid. Gravity must now be turned ON . Press the Play button, allow the Satellite to move through one orbit, and then press Pause. Make note below of the Orbital Time. Carefully slide the satellite to the right by the distance D to the 2D spot. Again, press Play and capture the time of the 2 nd orbit. Repeat for 3D, 4D, and 5D. Record your data in the Table below. 8A. (25 points total) Heigh t ORBITAL TIME 1D 92 minutes 2D 225 minutes 3D 606 minutes 4D

ASTR 110L Lab 07 5D 8B. Describe the changes in the orbits from the first to the fifth. (10 points total) The orbit of the planet moved away from the earth and its gravitational pull. The further the orbit starts the less effect the gravitational pull has an effect on it’s inertia. *************************************************************** EXTRA CREDIT. 8C. The Velocity hadn’t increased, but the orbits went successively higher. This seems paradoxical and to violate common sense. PROVIDE A RATIONALE FOR THIS CURIOUS PHENOMENON. Velocity is a direct consequence of the gravitational force that varies with the distance, according to newtons law of universal gravitation. The force between two objects is directly proportional to the product of their masses, inversely proportional to the square of the distance between their centers, the further the satellite moved away, the force between is decreased.

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Lab 07 - WorkSheet-1

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