QUESTION 2 Official names and orbital information for solar system objects Planet Perihelion - Aphelion (AU) PLANET Orbital Eccentricity Mercury 0.307 - 0.466 0.205 Venus 0.718 - 0.728 0.007 Sun (Focus) Earth 0.983 - 1.016 0.016 Mars 1.381 - 1.665 0.093 Jupiter Saturn 4.951 - 5.455 0.048 9.020 - 10.053 0.054 Aphellion Uranus 18.286 - 20.096 0.047 Perihelion Neptune 29.810 – 30.327 0.008 Using the perihelion and aphelion measurements, as well as the eccentricity value, find the polar equation that defines an elliptical orbit of the planet that you selected. Upload your work and an equation. Attach File Browse My Computer QUESTION 3 Using the perihelion and aphelion measurements (from the table from part 2) of your planet, find the polar equation for an ovular orbit, as defined by Cassini. Upload your work and an equation. Attach File Browse My Computer QUESTION 4 Using the polar equation (of the elliptical orbit) that you found in part 2 of this lab, and what you learned in this chapter, estimate the distance traveled in one complete orbit around the Sun. Upload your work and answer. Attach File Browse My Computer

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question 1

Other than Mercury and Pluto (since Pluto's not a planet), choose one of the planets.

Question 2-4, see attached

In this chapter, you learned that Johannes Kepler played an important role in describing planetary motion. In his research, he provided strong arguments for the elliptical trajectory of the planets around the Sun.
In 1675, a French Astronomer by the name of Giovanni Domenico Cassini did not agree with Kepler and tried to prove that the planetary orbits were not elliptical, but ovular.
ер
Remember that the polar equation for an ellipse is r =
when the directrix is perpendicular to the polar axis and the Focus (the Sun, in this case) is at the Pole, with eccentricity e.
1 - ecose
Directrix
F(0, 0)
The Cassini Oval has the polar equation:
4 - 2c?r?cos(20) + c* - a4 = 0.
Notice in the following image that when the eccentricities are small (less than 0.2), the differences in the graphs of each of these shapes are quite insignificant.
Transcribed Image Text:In this chapter, you learned that Johannes Kepler played an important role in describing planetary motion. In his research, he provided strong arguments for the elliptical trajectory of the planets around the Sun. In 1675, a French Astronomer by the name of Giovanni Domenico Cassini did not agree with Kepler and tried to prove that the planetary orbits were not elliptical, but ovular. ер Remember that the polar equation for an ellipse is r = when the directrix is perpendicular to the polar axis and the Focus (the Sun, in this case) is at the Pole, with eccentricity e. 1 - ecose Directrix F(0, 0) The Cassini Oval has the polar equation: 4 - 2c?r?cos(20) + c* - a4 = 0. Notice in the following image that when the eccentricities are small (less than 0.2), the differences in the graphs of each of these shapes are quite insignificant.
QUESTION 2
Official names and orbital information for solar system objects
Perihelion - Aphelion
Planet
PLANET
Orbital Eccentricity
(AU)
Mercury
0.307 - 0.466
0.205
Venus
0.718 - 0.728
0.007
Sun (Focus)
Earth
0.983 – 1.016
0.016
Mars
1.381 - 1.665
0.093
Jupiter
4.951 - 5.455
0.048
Saturn
9.020 - 10.053
0.054
Aphelion
Uranus
18.286 – 20.096
0.047
Perihelion
Neptune
29.810 - 30.327
0.008
Using the perihelion and aphelion measurements, as well as the eccentricity value, find the polar equation that defines an elliptical orbit of the planet that you selected.
Upload your work and an equation.
Attach File
Browse My Computer
QUESTION 3
Using the perihelion and aphelion measurements (from the table from part 2) of your planet, find the polar equation for an ovular orbit, as defined by Cassini.
Upload your work and an equation.
Attach File
Browse My Computer
QUESTION 4
Using the polar equation (of the elliptical orbit) that you found in part 2 of this lab, and what you learned in this chapter, estimate the distance traveled in one complete orbit around the Sun.
Upload your work and answer.
Attach File
Browse My Computer
Transcribed Image Text:QUESTION 2 Official names and orbital information for solar system objects Perihelion - Aphelion Planet PLANET Orbital Eccentricity (AU) Mercury 0.307 - 0.466 0.205 Venus 0.718 - 0.728 0.007 Sun (Focus) Earth 0.983 – 1.016 0.016 Mars 1.381 - 1.665 0.093 Jupiter 4.951 - 5.455 0.048 Saturn 9.020 - 10.053 0.054 Aphelion Uranus 18.286 – 20.096 0.047 Perihelion Neptune 29.810 - 30.327 0.008 Using the perihelion and aphelion measurements, as well as the eccentricity value, find the polar equation that defines an elliptical orbit of the planet that you selected. Upload your work and an equation. Attach File Browse My Computer QUESTION 3 Using the perihelion and aphelion measurements (from the table from part 2) of your planet, find the polar equation for an ovular orbit, as defined by Cassini. Upload your work and an equation. Attach File Browse My Computer QUESTION 4 Using the polar equation (of the elliptical orbit) that you found in part 2 of this lab, and what you learned in this chapter, estimate the distance traveled in one complete orbit around the Sun. Upload your work and answer. Attach File Browse My Computer
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