Well of course matching it’s orbit. That’s what rendezvousing is all about. You launch so that you match the orbit of the satellite. You’re in the same orbit and you match the velocity of the vanguard and move up to it and pick it up. I know it’s not as simple as that but it’s not like we would just launch up to the perigee and try to snatch it as it comes zipping by. That would be stupid.
One of the problems would be that the Vanguard’s orbit is very elliptical and goes through the radiation belts 2 times each orbit. So you would have a manned spacecraft passing through the radiation belt as many times as it would take to achieve rendezvous, and return to low earth orbit, or land.