[demallien]

Orbits are not intuitive. To head "downwards", you have to slow down your orbital velocity, which reduces the radius of the orbit. In other words you have to decelerate. When you do the maths, you actually have to decelerate more from Earth orbit to get to the sun than you do to accelerate up to solar escape velocity.

[redcalx]

Right, so an orbit implies an amount of kinetic energy which you need to lose to lower your orbit; and losing kinetic energy in a frictionless environment requires some kind of propulsion.