Universe
11th Edition
ISBN: 9781319039448
Author: Robert Geller, Roger Freedman, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 4, Problem 27Q
(a)
To determine
The semi-major axis of an ellipse in which the Sun as at one of the foci and Earth and Mars are at the perhelion and aphelion respectively. It is given that a spacecraft launched from Earth reaches Mars by travelling along this ellipse.
(b)
To determine
The time taken by a spacecraft to travel to Mars along an ellipse, with the Sun at one of the foci and Earth and Mars at the perhelion and aphelion, respectively.
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one trajectory that can be used to send spacecraft from earth to mars is an elliptical orbit that has the sun at one focus, its perihelion at earth, and it's aphelion at mars. the spacecraft is launched from earth and coasts along this ellipse until it reaches mars, when a rocket is fired to either put the spacecraft into orbit around mars or cause it to land on mars. (a) find the semimajor axis of the ellipse (in au). (hint: draw a picture showing the sun and the orbits of earth, mars, and the spacecraft. treat the orbits of earth and mars as circles.) [enter your answer in units of au]
Like all planets, the planet Venus orbits the Sun in periodic motion and simultaneously spins about its axis. Just as on Earth, the time to make one complete orbit (i.e., the period of orbit) is what defines a year. And the time to make one complete revolution about its axis (i.e., the period of rotation) is what defines a day. The period of orbit for the Earth is 365.25 days and the period of rotation is 24 hours (1.00 day). But when these same values for Venus are expressed relative to Earth, it is found that Venus has a period of orbit of 225 days and a period of rotation of 243 days. So for Venus inhabitants, a day would last longer than a year! Determine the frequency of orbit and the frequency of rotation (in Hertz) on Venus.
The semimajor axis of Mars orbit is about 1.52 astronomical units (au), where an au is the Earth's average distance from the Sun, meaning the semimajor axis of Earth's orbit is 1 au. To go from Earth to Mars and use the least energy from rocket fuel, the orbit has a semimajor axis of 1.26 au and an eccentricity of about 0.21. Starting at Earth's orbit, to follow this path we give the spacecraft an orbital velocity of 40 km/s. Which of the following describes this best?
a. It arrives at Mars orbit at the same moment that Mars is there, and must speed up to go into an orbit next to Mars or else drop back into perihelion (closest to the Sun) at Earth's orbit.
b. It arrives at Mars orbit at the same moment that Mars is there, and must slow down to go into an orbit next to Mars or else drop back into perihelion (closest to the Sun) at Earth's orbit.
c. It flys past Mars on its trajectory unless it is braked by accelerating toward the Sun. It which leaves Earth when Mars is nearly…
Chapter 4 Solutions
Universe
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