Question

3. In interplanetary exploration, elliptical transfer orbits, like the one shown from Earth to Mars, allow space probes to reach the intended destination using a minimum of fuel. (Such orbits are called Hohmann transfer orbits.) Note: Assume the orbits of Earth and Mars about the Sun are circular with radii 1.000 AU and 1.524 AU, respectively. Ignore any effects due to the rotation of the Earth a. Describe qualitatively the maneuvers required PM TE Sun for the probe upon entering and leaving the transfer orbit. That is, must the probe increase or decrease its speed (i) upon entering the transfer orbit at point 1? (i) upon entering Mars orbit at point 2? Explain Earth orbit Mars orbit Transfer orbit b. Determine the following quantities * the semimajor axis, eccentricity, and latus rectum of the transfer orbit . the time required for the probe to travel from point 1 to point 2 along the transfer orbit (Note: When measuring time in units of earth-years and distance in AU's, the quantity 4/GMsun has a value of unity.) It is said that interplanetary expeditions can be launched at only certain times, or "launch opportunities." In light of your results from part b above, explain what is meant by this statement c.

Answer 1

the velocl of the sate ti to at point 1' mus the # have Marss ssi tia apog of the tosfer orkit that onelt sun, ile tranger arbit amd mons welser Heee amina ns for tio ansfer obit ve local at point2 setallitawow TE a it sevolwe in the cictan oot, than veloeli e foint so, tha chama in delae o etr it YE n ount toe man ve to cili at to entax into thaoBit So, uoe tact in sun uskicht nt point 2 tCrough point 2 So tha desiadve lo c lar oleiじ change in veto So to ent en "tha circu , at poht

b). Semi. major axisa»E2. 2.524 Au 1,262 AU act that a(1 -e a. 1-262 Abo 드) C, 1231 AU A U 262 = 2.413 AU 446 namn 3/ A0 2! the period So tho timo of f

postion o ima ti Cas ile. tivna of aumd) Mans. Aho, E af satet above, doent happon ev sone speci fie time . Then せ