NASA sends a satellite to another planet by placing the satellite in a Keplerian

Question

NASA sends a satellite to another planet by placing the satellite in a Keplerian orbit (around the sun) such that the perihelion is at the radius of the Earth's orbit (1 AU) and the aphelion is at the radius of the planet's orbit. Most of the trip is just free fall in the sun's gravitational field. The small gravitational effects of Earth mid the other planet, which only affect the satellite at the very beginning and end of the trip, may be neglected. Suppose a new planet, call it Questerion. were to appear in the Solar System, in a circular orbit of radius 7.00 AU. Calculate the time it would take a NASA satellite to travel from Earth to Questerion. Express the result in years. Tries 0/25

Explanation / Answer

find the semi major axis of the orbit, or the average distance from the sun. =4.4 AU, which is 1.2267E12 m=a

Then plug this into T=sqrt(pi^2 (a)^3/(G*M))

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