In the 1920\'s the German engineer Walter Hohmann proposed a simple and efficien

ID: 801656 • Letter: I

Question

In the 1920's the German engineer Walter Hohmann proposed a simple and efficient route to move between planets (an "orbital transfer"). The transfer orbit (shown below) is an ellipse whose perihelion is at the orbit of the inner planet (Earth) and whose aphelion is at the orbit of the outer planet (Mars). This requires only two engine burns: one when leaving Earth and the other when arriving at Mars. The rest of the time the spacecraft is "coasting" on a Newtonian orbit. It is also economical, using less fuel than a hyperbolic orbit which could more quickly reach Mars. A drawback is that this transfer requires careful timing. The spacecraft must reach its aphelion just as Mars is also reaching this point. This "launch window" to Mars opens every 2.1 years (the synodic period of Mars).

For this problem you can find solar system data (masses, orbital periods, semimajor axes) in Appendix C on page 1279.

(a) What is the length of the semimajor axis and orbital period of the Hohmann transfer orbit from Earth to Mars? (Show your work and give an answer in AU and Earth years.)

(b) Using the Hohmann orbital transfer in part (a), how long will the trip from Earth to Mars take?

(c) The average orbital speed v for a given orbit is given by: v = 2?a/P where a is the semimajor axis and P is the orbital period. What is the change in orbital speed ?v needed for the spacecraft when it is leaving Earth and when it is arrive at Mars?

Mars Transfer Earth Orbit Sun

Explanation / Answer

a.Hohmann transfer is an elliptical orbit that requires minimum energy and used to transfer two astronomical bodies of circular orbits having different radii in the same plane.

according to kepler's third law:

T2/a3= constant

P2/a3=1

P2=a3

P=1.41years

Now a3=??

(1.41)^2=a3

1.981=a3

a=1.2

Vorbit=2pi/P

P=1.4 years

Vorbit=2*3.14/1.4

=4.4 years

orbital period=4.4 years

b. The trip from earth to Mars will take half the time the total trip=P/2

P=1.4 years/2

=0.7 years

Navigate

In the 19 th Century one idea of how the Sun produced its energy assumed it was

In the 1920s, Arthur Boycott discovered the first maternal effect phenotype in t

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.

In the 1920\'s the German engineer Walter Hohmann proposed a simple and efficien

Question

Explanation / Answer

Related Questions

Navigate