Your spacecraft will never be under the influence of the Sun only. But you might consider the Hill Sphere as the place where you've left Earth's influence. Even deep in Earth's Hill Sphere, you're still on a hyperbolic trajectory the moment you complete your burn.<br /><br />Calculate how much delta v you need to get from the orbit of Earth to the orbit of Mercury. Then use the formula sqrt(2GM/r + v), where v is the delta v you just computed, M is the mass of the Earth (5.97e24) and r is your distance from Earth in a circular orbit. This calculates how much delta v you need to escape Earth, and give you the required extra velocity to reach Mercury's orbit. Make sure you perform your burn such that your trajectory away from Earth is in line with Earth's orbital motion in a retrograde direction. And do it at the right time of year so that when you reach the orbit of Mercury, Mercury is there waiting for you.