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Hohmann Transfer Orbit Applet

 The applet computes and displays the orbit of a spacecraft sent off from the Earth's orbit to travel to an inner or outer planet of the solar system. The transfer orbit is treated as a simple Keplerian ellipse around the Sun. The perturbations by the Earth, the target planet, and all the other bodies in the Solar system are neglected. The orbits of the Earth and the target are both supposed to be circular, inclination of the orbit against the plane of the Earth is neglected. In 1925 Walter Hohmann (1880-1945) recognized that the minimum energy orbit between two circular orbits is an ellipse which is tangent at the perihelion of one orbit and at the aphelion of the other.

The launch is in the direction of the of the origin planet's orbit to take advantage of its kinetic energy.

To reach an outer planet:
-  a velocity greater than the orbital velocity of the Earth is required: positive launch burn : ∆v>0
-  the arrival velocity of the Hohmann orbit is smaller than the orbital velocity of the target planet's velocity,
a soft landing requires a
positive arrival burn: ∆v>0

To reach an inner planet:
-  a velocity smaller than the orbital velocity of the Earth is required: negative launch burn : ∆v<0
-  the arrival velocity of the Hohmann orbit is greater than the orbital velocity of the target planet's velocity,
a soft landing requires a negative arrival burn: ∆v<0

In case of the Sun as the target the orbital radius at arrival is supposed to be the radius of the Sun (to avoid infinities).

 Select from the Target menu: Display options

 from Earth to Sun to Mercury to Venus to Mars to Jupiter to Saturn orbital radius 1 AU 0.0050 AU 0.3871 AU 0.723 AU 1.524 AU 5.204 AU 9.582 AU orbital period 365.24 d 0.1 d 88.0 d 224.7 d 687.0 d 4332.6 d 10833.9 d orbital velocity 29.79 km/s 436.6 km/s 47.88 km/s 35.03 km/s 24.13 km/s 13.06 km/s 9.62 km/s launch velocity 2.87 km/s 22.25 km/s 27.32 km/s 32.74 km/s 38.58 km/s 40.09 km/s launch burn -26.92 km/s -7.53 km/s -2.47 km/s 2.95 km/s 8.79 km/s 10.30 km/s transfer orbit s-m axis 0.502 AU 0.694 AU 0.862 AU 1.262 AU 3.102 AU 5.291 AU transfer orbit eccentricity 0.991 0.442 0.160 0.208 0.678 0.811 transfer orbit path length 1.03 AU 2.07 AU 2.69 AU 3.92 AU 8.51 AU 13.40 AU transfer time 65.0 d 105.5 d 146.1 d 258.9 d 997.8 d 2222.7 d arrival velocity 616.0 km/s 57.49 km/s 37.73 km/s 21.48 km/s 7.41 km/s 4.18 km/s arrival burn -179.4 km/s -9.61 km/s -2.71km/s 2.65 km/s 5.64 km/s 5.44 km/s

Earth - Moon Transfer Orbit:

 Flight Time Hohmann 119.5 h Jules Verne, Science Fiction 97.3 h Apollo 11, after Trans Lunar Injection Burn 72.0 h

Details for Earth-Mars Transfer and Return:

The "Target Mars" option only is including the return flight from Mars to Earth

 Start from Earth, t=0 Mars is 44.3° ahead Arrival at Mars, t = 258.9 days Earth is at 255.2° Waiting for 454.1 days, t = 713.1 days Earth is at 342.8° Arrival on Earth, t = 970.8 days

 Web Links Hohmann Transfer Walter Hohmann: The Attainability of Heavenly Bodies (PDF) Walter Hohmann’s Roads In Space (William I. McLaughlin) Lecture L17 - Orbit Transfers and Interplanetary Trajectories Apollo 11 (Wikipedia) Books Konstantin Ziolkowski: Die Erforschung des Weltraums mit Rückstoßgeräten; 1903. Walter Hohmann. Die Erreichbarkeit der Himmelskörper, 3. Auflage, Oldenbourg, München und Wien 1994, ISBN 978-3486231069 Hermann Oberth: Die Rakete zu den Planetenräumen, 1923. Nachdruck: Michaels-Verlag, 1984, ISBN 3-89539-700-8 Hermann Oberth: Wege zur Raumschiffahrt, Dritte, stark erweiterte Auflage von "Die Rakete zu den Planetenräumen",  1929. Nachdruck VDI Verlag 1986, ISBN 3-18-400755-3 Willy Ley (Hrsg.): Die Möglichkeit der Weltraumfahrt, Hachmeister & Thal, Leipzig 1928. Rudolf Nebel: Raketenflug, 1932. Microsoft Word - Tsiolkovsky_Bibliography.doc Max Valier: Der Vorstoß in den Weltraum, Oldenbourg, München und Berlin, 1. Auflage 1924. Max Valier: Raketenfahrt, Oldenbourg, München und Berlin, 5. Auflage 1928 Otto Willy Gail: Physik der Weltraunfahrt; Reich Verlag, München 1948.   Willy Ley: Vorstoss ins Weltall, Rakete und Raumschiffahrt; Universum Verlagsgesellschaft, Wien 1949. Science Fiction Jules Verne: De la Terre à la Lune, Trajet direct en 97 heures 20 minutes; 1865 Jules Verne: De la Terre à la Lune, Trajet direct en 97 heures 20 minutes; 1865 (PDF) Otto Willy Gail: Der Schuß ins All, Ein Roman von morgen; Breslau 1925 Otto Willy Gail: Der Stein vom Mond, Kosmischer Roman; Breslau 1926