It’s the foundational principle of “Launch Windows.” Because the earth rotates the sun and also spins on an axis, we can launch at a time of day that gives us time to accelerate and then leave earth orbit in the direction of earth’s orbit around the sun with minimum amount of energy required. The majority of energy used is simply to escape Earth orbit. Once orbiting the sun, comparatively very little energy would be required to approach it utilizing it’s own gravity.
During Perihelion the sun is 147100632 KM away, as the distance from the sun is not constant for earth’s orbit.
It requires energy to shrink an orbit just as it does to grow it. Since we’re launching from Earth, we start with Earth’s orbit around the sun, and we have to burn enough to bring the perihelion of our launched child’s solar orbit to within the sun itself. We could use Venus or Mercury for gravity assists but the angular speed of the orbit does have to be mostly cancelled to hit the sun
It’s still a lot cheaper than instantaneously cancelling angular velocity.
