Understanding Planetary Orbits: Experiments and Results

PHYS1160 EXPERIMENT RESULTS 1a) What is the shape of the orbit of the planet? - Perfect circular orbit 1b) How many Earth days does it take to complete one orbit? - 365 days 1c) Which planet in our Solar System does this represent? - Planet Earth 2) Take a screen capture of the orbit

4) Change the mass of the planet to whatever mass you like and replay the orbit, pausing when one orbit has completed. (changed the ‘mass of the planet’ to 1.5x original mass) 4a) What happens to its orbit? - The orbit is unchanged and continues to orbit as a perfect circle around the sun 4b) How is the orbit different to the first case? - The orbit is not different to the first case. It remains the exact same regardless of the change in the mass of the planet. 4c) If it is different, why is it different? - It is not different – N/A 4d) Take a screen capture of the orbit.

5. Shorten the length of the velocity arrow (also called a vector) by clicking on the circled v and making the arrow shorter. Ensure that the planet still completes a full orbit. 5a) Take a screen capture of the orbit. 5b) What is the new orbital period of the planet? - 246 days 5c) How did the shape of the orbit change? - The shape of the orbit is still a perfect circular motion; however, the orbit is much smaller and has a closer path on the left-hand side of the sun to that of the right-hand side. This means the ‘period’ of the orbit has decreased. 5d) Why did it change? - Decreasing the velocity of an orbiting planet changes the shape of the orbit in accordance with Kepler's laws because a slower orbital speed alters the balance between kinetic and potential energy. Kepler's second law states that a planet sweeps equal areas in equal times, and when the velocity decreases, the planet spends more time in regions closer to the

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central body. This elongates the orbit, adhering to Kepler's first law, which describes orbits as ellipses with the central body at one of the ends of the orbit. 5e) How did the length of the velocity arrow change throughout a full orbit? What does this mean? - As the orbiting planet moved closer to the Sun, the centre planet, the velocity arrow of the planet gets larger indicating that it’s getting faster. This is due to the orbital path being very close to the Sun, and therefore the gravitational force is at its highest. 5f) Which of Kepler’s laws explains this? - According to Kepler's laws, the velocity of an orbiting planet changes due to the conservation of angular momentum. Kepler's second law states that a planet sweeps out equal areas in equal times, meaning it moves faster when closer to the central body (like the Sun) and slower when farther away. As the planet moves along its elliptical orbit, the changing distance from the central body causes the velocity to vary, adhering to the conservation of angular momentum principle. 6a) Note whether the gravity vector/arrow is the same for the planet and the Sun or not. - The gravity vector/arrow is the exact same for the planet and the Sun. As the orbiting planet goes around the Sun, the gravity vector between the two planets is perfectly opposite to each other whilst being in complete harmonious rhythm. 6b) Note whether the velocity vector/arrow is the same for the duration of the planets orbit. - As the orbiting planet moved closer to the Sun, the centre planet, the velocity arrow of the planet gets larger indicating that it’s getting faster. This is due to the orbital path being very close to the Sun, and therefore the gravitational force is at its highest. 6c) Also note whether the Sun appears to move as the planet orbits.

- The Sun does NOT appear to move as the planet orbits. 7. Turn gravity force (not gravity!) off. Change the mass of the star to whatever mass you like and replay the orbit, pausing when one orbit has completed . (changed the ‘mass of the star to 1.5x original mass) 7a) What happens to its orbit? - The entire shape of the orbit alters changing from a perfect circular motion to that of an elliptical orbit. As the orbiting planet reaches the furthest away point from the star within the orbit it reaches its ultimate slowest velocity, however as it reaches closest to the star it approaches its maximum velocity. (evident through increasing/decreasing velocity vector) 7b) How is the orbit different to the other cases? - The differentiating factor between other cases is the shape of the orbit to that of an elliptical orbit from a circular one. The orbit also decreases in size as well as the amount of days to complete a full orbit to 156 days. 7c) If it is different, why is it different? - Increasing the mass of the star changes the orbiting planet's orbit shape according to Kepler's laws due to the altered gravitational force. Kepler's third law states that the square of a planet's orbital period is proportional to the cube of the semi-major axis of its orbit. If the star's mass increases, the gravitational force pulling the planet intensifies, leading to a shorter semi-major axis and a more compact, elliptical orbit, as described by Kepler's first law. 7d) Take a screen capture of the orbit.

8. Click the ‘gravity force’ button. 8a) Note whether the gravity vector/arrow is the same for the planet and the Sun or not. - The gravity vector is the same magnitude for both planets, however the direction in which the force is applied is the polar opposite. 8b) Note whether the velocity vector/arrow is the same for as the planet orbits. - As the orbiting planet moved closer to the Sun, the centre planet, the velocity arrow of the planet gets larger indicating that it’s getting faster. This is due to the orbital path being very close to the Sun, and therefore the gravitational force is at its highest. 8c) Also note whether the Sun appears to move as the planet orbits. - No, the sun does NOT appear to move as the planet orbits PRELIMINARY RESULTS 9. Switch to the planet and moon scenario. 9a) Does the planet move as the moon orbits? - Yes, the planet does seem to slightly move as the moon orbits. The planet seems to oscillate to a small degree 9b) How is this different to the Sun-planet scenarios above? - In this scenario, the central planet moves as the orbiting planet goes around it. However, in the Sun-planet scenario, the Sun appears to stay completely stationary throughout the entire orbit.

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9c) Where are the centres of mass in each scenario from Questions 1, 4, and 7? - The centre of mass in each of these questions is the Star (Sun) 11. Take the star and planet in the standard configuration to be the Sun and the Earth. 11a) When the gridlines are turned on, what is the distance between each marking, in AU? - Using the measuring tape tool, the distance portrayed: 73742686 km 73742686 km = 0.492939409197 AU = 0.5 AU 13. Alter the velocity arrow until circular paths are created for each of the planet orbital distances that you chose. Click the rewind button to make changes until you get it right. Take a screenshot of every orbit that you record. NB: It doesn’t need to be perfect; it just needs to be very close! #1 #2 #3

#4 14. Record the time it takes each planet at those orbital distances to complete one orbit, in a table like the one below. Planet Distance (AU) Orbital Period (days) # 1 0.75 177 2 1.5 340 3 0.5 237 4 0.25 62 14a) Do these results follow Kepler’s third law? Planet Distance (AU) Orbital Period (days) - Kepler’s 3 rd Law states that, “ a planet’s orbital period is proportional to the size of its orbit (its semi-major axis) ” in which the cases above prove to follow this law. The further the orbiting planet deviated from the Sun, in #2 for example, where the distance was at 1.5 AU – the period increased to that of 340 days. However, once decreased to 0.25 AU in #4, the orbital period proportionally decreased to 62 days, thus proving to follow Kepler’s 3 rd Law.

15) Which planet in our Solar System do you expect to have the fastest orbital velocity? - Mercury, being the closest planet to the Sun would experience the strongest gravitational pull from the Sun. This proximity results in Mercury having the fastest orbital velocity of any planet in our Solar System. 15a) Which planet would you expect to have the slowest orbital velocity? - I would expect the planet with the slowest orbital velocity in our Solar System to be Neptune. Orbital velocity depends on the distance from the Sun, and Neptune is the eighth and farthest known planet from the Sun and would therefore be the slowest. Its large distance from the Sun and the corresponding weaker gravitational influence would contribute to a relatively slow orbital speed. 15b) What is the reason for this? Kepler’s Laws of Planetary Motion - Fastest: In our Solar System, the orbital velocity of a planet depends on its distance from the Sun and the mass of the Sun. According to Kepler's laws of planetary motion, the farther a planet is from the Sun, the slower its orbital velocity, and the closer it is, the faster its orbital velocity. - Slowest: According to Kepler's laws of planetary motion, planets that are farther from the Sun have slower orbital velocities. Neptune, being located at a further distance from the Sun than any other planet, experiences weaker gravitational pull compared to inner planets like Mercury (closest planet). As a result, Neptune has a slower orbital speed.

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16) What did you learn in this experiment? - I learnt the direct correlation of Keplers Laws of Planetary Motion and how changing different aspects, such as the velocity, mass and even distance create differing results which are all concepts understood under these laws. By understanding Kepler's laws of planetary motion provides insights into the fundamental principles governing the motion of celestial bodies. Kepler's laws explain the elliptical nature of planetary orbits, the relationship between a planet's orbital period and its distance from the central body, and the equal area law. By acquiring this knowledge, and tinkering with values via the website, enhances our comprehension of the dynamics of planetary systems especially those of that within our solar system.

PHYS1160 EXPERIMENT RESULTS

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