On circular orbit burning prograde/retrograde makes the orbit elliptical with raising or lowering the orbit on the opposite side of the body, making the burn position the new periapsis/apoapsis respectively.

Now, burning radial or antiradial makes the orbit an ellipse as well, but by changing simultaneously the apoapsis and periapsis. In some cases the new shape of the orbit may be desirable (e.g. setting up a bielliptical transfer). In other (in reverse) it could help circularize an elliptical orbit to a given altitude if its periapsis and apoapsis are on two sides of that altitude.

Is there a specific reason? Is it considerably less efficient than a combination of prograde/retrograde burns setting up the same orbit, or something like that?

Burning prograde at periapsis to start the bi-elliptic transfer takes advantage of the Oberth effect, so it's generally advantageous to arrange that the orbit is near-circular or that the pre-burn orbital periapsis is at the same angle as the transfer orbit periapsis.

Likewise, if you're inserting into orbit at the other end of the bi-elliptic (as opposed to doing a flyby), it's most efficient to do that by burning retrograde at the target's periapsis (in the target's frame of reference, of course, rather than the origin's).

If the desired final orbit isn't circular, of course, the insertion burn may have a substantial radial/antiradial component, but the retrograde portion of the ∆v vector is generally dominant.

Generally, the only time you'd want to burn radial/antiradial is if you're in an elliptical orbit and need to change the orientation of the ellipse.

• For bi-elliptic, wouldn't bringing your current periapsis way lower be advantageous, granting even more Oberth effect (before bringing the apoaxis far&high)?
– SF.
Jun 25, 2015 at 15:12
• In general, your starting orbit will always be as low as practical. It would be better to launch direct to the transfer trajectory than to launch to 500km, circularize, then dip back to 100km for the transfer, e.g. (Unless you're talking about, like, Earth to low solar orbit (for Oberth) to Mars, which is above my pay grade.) Jun 25, 2015 at 15:23
• That's for LEO->up. What about Earth->Jupiter? Wouldn't dropping the periapsis towards Mercury be beneficial?
– SF.
Jun 25, 2015 at 15:48
• Burn antiradial from Earth's solar orbit, giving you a low perihelion while simultaneously raising aphelion, then burning for Oberth at solar periapsis to get apo to Jupiter orbit? I know we've used Venus for gravity assist to the outer planets, so I assume that's more beneficial than a very low perihelion, but you might want to ask it as a separate question. Jun 25, 2015 at 16:25