Aspacecraft has an orbit that just grazes earth's orbit at aphelion and just grazes venus's orbit at perihelion. assuming that earth and venus are in the right places at the right times, how long will the spacecraft take to travel from earth to venus?

The answer is The perihelion separation of the exchange circle that keeps running among Earth and Mars is 1.0 AU and the aphelion remove is 1.524 AU. Along these lines, the semi-significant hub of the circle would be (perihelion+aphelion)/2= 1.26 AU.  

Explanation:

Perihelion and Aphelion: Mercury circles the Sun at a normal separation (semi-real hub) of 0.387 AU (57,909,050 km; 35,983,015 mi). Be that as it may, because of its capriciousness of 0.205 – the most astounding in the Solar System, except for Pluto (0.248) – its separation from the Sun extends extensively. Mars has an exceptionally offbeat circle; that is, it goes amiss from an immaculate hover more than some other planet's circle At its most remote separation (aphelion), Mars is 154 million miles (249 million km) from the sun. At its nearest (perihelion), Mars is 128 million miles (206 million km) far off.

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