A m nimm-enegy transter oit to an outer planet corsists of puttig a spaceratt on

Question

A m nimm-enegy transter oit to an outer planet corsists of puttig a spaceratt on an elliptical trajectory with the departure plant cespnding to the perihelion of the e pse, or the closest point to the Sun, and he arrival olsner at the sphelion, or the fartrest port from tre sur. (Assume the orb ta rad us of the Earth is 50 x 1011 m, and the oroltel raclus of Mers ls 2.28 x 1011 m.) Transfer orbit Mars orbit Arrival at Mars Launch fronm the Earth Sun Earth orbit. (a) Use Kepler's third la to calculate how long it would take to go fron Earth to Mars on such an orbit as shown in the figure above yr (Can such an orbit be undertaken at any time? Yes No Explain

Explanation / Answer

This answer yields rough esteems. Exact vitality prerequisites would require full orbital parameters, decision of proper flight and goal focuses, (for example, Earth-L2, Mars-L1, and so on.), and motor sort and effectiveness as data sources.

* perihelion distance: 1 AU (earth)

* aphelion distance: 1.523 AU (mars)

in this way,

length of semi-major axis of the exchange orbit = (1 + 1.523)/2

= 1.2615 AU

As per Kepler's law,

Orbital time of transfer orbit= sqrt( 1.2615^3 ) = 1.4168 years.

the real transfer is 1/2 of this.

trip time earth to mars = 0.708 years

b) No, this orbital transfer must be made when earth and mars will be at the perfect place in their circles regarding each other, generally the orbital transfer will put the craft in a mars orbit out-of-stage with mars.

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