Homework Help is Here – Start Your Trial Now!
Science
Advanced Physics
1. 2. 3. You have decided to join the ranks of Absurdly Rich Space Tourists (ARST) and go on a wonderful vacation to Mars and back. That should make all the other ARST insanely jealous since you are going to Mars and they never even got into Earth orbit. For the orbital dynamics part of your vacation planning assume that Earth is in a circular orbit 1.00 AU from the Sun, Mars is in a circular orbit 1.52 AU from the the Sun, and that the the orbits are coplanar. The orbit you plan to use for your trip is an ellipse with the Sun at one focus (Kepler's 1st Law). The perihelion of the ellipse is at Earth's orbit at 1.00 AU and the aphelion is at Mars' orbit at 1.52 AU. Your spacecraft will go around the Sun in the same sense as Earth and Mars. The orbit you have chosen for your trip is called a Hohmann Transfer Orbit. For this problem assume that the orbital period of Earth is 365 days and the orbital period of Mars is 684 days. Check that Kepler's Third Law holds for Earth and Mars. What is the semi-major axis a of the spacecraft's orbit? What is the eccentricity e of the spacecraft's orbit? What is the orbital period of the spacecraft? How long does it take to get to Mars? How long does it take to get from Mars to Earth?

1. 2. 3. You have decided to join the ranks of Absurdly Rich Space Tourists (ARST) and go on a wonderful vacation to Mars and back. That should make all the other ARST insanely jealous since you are going to Mars and they never even got into Earth orbit. For the orbital dynamics part of your vacation planning assume that Earth is in a circular orbit 1.00 AU from the Sun, Mars is in a circular orbit 1.52 AU from the the Sun, and that the the orbits are coplanar. The orbit you plan to use for your trip is an ellipse with the Sun at one focus (Kepler's 1st Law). The perihelion of the ellipse is at Earth's orbit at 1.00 AU and the aphelion is at Mars' orbit at 1.52 AU. Your spacecraft will go around the Sun in the same sense as Earth and Mars. The orbit you have chosen for your trip is called a Hohmann Transfer Orbit. For this problem assume that the orbital period of Earth is 365 days and the orbital period of Mars is 684 days. Check that Kepler's Third Law holds for Earth and Mars. What is the semi-major axis a of the spacecraft's orbit? What is the eccentricity e of the spacecraft's orbit? What is the orbital period of the spacecraft? How long does it take to get to Mars? How long does it take to get from Mars to Earth?

icon
Related questions
Question

Astronomy 

1. 2. 3. 4. 5. 6. 7. 8. 9. SPACEFLIGHT - A TRIP TO MARS AND BACK You have decided to join the ranks of Absurdly Rich Space Tourists (ARST) and go on a wonderful vacation to Mars and back. That should make all the other ARST insanely jealous since you are going to Mars and they never even got into Earth orbit. For the orbital dynamics part of your vacation planning assume that Earth is in a circular orbit 1.00 AU from the Sun, Mars is in a circular orbit 1.52 AU from the the Sun, and that the the orbits are coplanar. The orbit you plan to use for your trip is an ellipse with the Sun at one focus (Kepler's 1st Law). The perihelion of the ellipse is at Earth's orbit at 1.00 AU and the aphelion is at Mars' orbit at 1.52 AU. Your spacecraft will go around the Sun in the same sense as Earth and Mars. The orbit you have chosen for your trip is called a Hohmann Transfer Orbit. For this problem assume that the orbital period of Earth is 365 days and the orbital period of Mars is 684 days. Check that Kepler's Third Law holds for Earth and Mars. What is the semi-major axis a of the spacecraft's orbit? What is the eccentricity e of the spacecraft's orbit? What is the orbital period of the spacecraft? How long does it take to get to Mars? How long does it take to get from Mars to Earth? When (at what Earth - Mars configuration) do you launch to go? In other words, where does Mars need to be relative to Earth in order for you to get to Mars successfully? Where is Earth when you arrive at Mars? Where does Earth need to be relative to Mars for you to return safely to Earth? How long to you have to wait on Mars before you can launch for home? What is your total trip time? Care to go? If you miss your launch configuration in question 4 or 6/7, how long do you have to wait for the next one?
Transcribed Image Text:1. 2. 3. 4. 5. 6. 7. 8. 9. SPACEFLIGHT - A TRIP TO MARS AND BACK You have decided to join the ranks of Absurdly Rich Space Tourists (ARST) and go on a wonderful vacation to Mars and back. That should make all the other ARST insanely jealous since you are going to Mars and they never even got into Earth orbit. For the orbital dynamics part of your vacation planning assume that Earth is in a circular orbit 1.00 AU from the Sun, Mars is in a circular orbit 1.52 AU from the the Sun, and that the the orbits are coplanar. The orbit you plan to use for your trip is an ellipse with the Sun at one focus (Kepler's 1st Law). The perihelion of the ellipse is at Earth's orbit at 1.00 AU and the aphelion is at Mars' orbit at 1.52 AU. Your spacecraft will go around the Sun in the same sense as Earth and Mars. The orbit you have chosen for your trip is called a Hohmann Transfer Orbit. For this problem assume that the orbital period of Earth is 365 days and the orbital period of Mars is 684 days. Check that Kepler's Third Law holds for Earth and Mars. What is the semi-major axis a of the spacecraft's orbit? What is the eccentricity e of the spacecraft's orbit? What is the orbital period of the spacecraft? How long does it take to get to Mars? How long does it take to get from Mars to Earth? When (at what Earth - Mars configuration) do you launch to go? In other words, where does Mars need to be relative to Earth in order for you to get to Mars successfully? Where is Earth when you arrive at Mars? Where does Earth need to be relative to Mars for you to return safely to Earth? How long to you have to wait on Mars before you can launch for home? What is your total trip time? Care to go? If you miss your launch configuration in question 4 or 6/7, how long do you have to wait for the next one?
Orbit of Mors Orbit of Earth Earth at Departure Kepler's Thir 2 Law. 3 (9) Az a₁ Perihelion: Aphelion: Гр A = Sun a = {(₁ + r) e = PA-re PA+rp a(1-e) a(lte) Mars at Arrival Kepler's Second Law - Circular Onkit 88= 360° ( 4 ) At: Elapsed Time so= Angle Orbited Through P = Orbital Period Closest to Sun Farthest from Sun Spacecraft Orbit Semi-Major Axis Eccentricity
Transcribed Image Text:Orbit of Mors Orbit of Earth Earth at Departure Kepler's Thir 2 Law. 3 (9) Az a₁ Perihelion: Aphelion: Гр A = Sun a = {(₁ + r) e = PA-re PA+rp a(1-e) a(lte) Mars at Arrival Kepler's Second Law - Circular Onkit 88= 360° ( 4 ) At: Elapsed Time so= Angle Orbited Through P = Orbital Period Closest to Sun Farthest from Sun Spacecraft Orbit Semi-Major Axis Eccentricity
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer