(Bill Bogen) wrote in
om:

But an object _could_ (very small chance, I admit) be in heliocentric
orbit and yet pass over the Earth at just the right speed to enter a
circular polar orbit at 20310.8 km radius, could it not? Without
having to shed any velocity at all?

I don't think so. If the object is passing over the Earth at the
right speed to "enter" an orbit, it's already *in* orbit.

To put it another way: Imagine filming this object and then running
the film backwards:
you'd see an object in orbit around the Earth suddenly leave orbit
without gaining any velocity, which is impossible. Since Newtonian
mechanics works the same whether time runs forwards or backwards, it
would also be impossible if you run the film forwards. Therefore
entering orbit without shedding velocity is impossible.

--
Dave Empey