# What is the least energy trajectory in Astronomy?

Hi I wanted to know what the least energy trajectory is in relation to astronomy as I can't seem to find a good answer on Google. I want to know because I am trying to answer this question:

A space probe is put into orbit around the sun with semi major axis of $$2AU$$. How long in years does it take to orbit the sun once? If it travelled directly in a least energy trajectory, how long would it take the space probe to get from earth to it's new orbit ?

I believe I have done the first step which is use keplers 3$$^{\text{rd}}$$ law so

$$T = \sqrt{2^3} = 2.82$$ years but I have no idea what the least energy trajectory is in order to finish the problem?

Thanks