This answer to Trajectory to get into orbit says:
In most real launches to low Earth orbit, the burn continues from liftoff until orbital insertion, without a coasting phase. Some (like Antares) do coast between the first stage and second stage burn; the exact design of the launcher determines which approach is more efficient.
and links to Spaceflight 101's Antares Launch Vehicle Information where the Antares LEO Flight Profile section says:
Antares lifts off from its launch pad two seconds after the AJ-26 engines of the first stage are ignited to allow some time for them to achieve full thrust and monitor their ignition performance. After a short vertical ascent, Antares performs a roll & pitch maneuver to align itself with its pre-planned ascent trajectory.
The first stage burns for 235 seconds and separates after a brief, 5-second post-burn coast. Stage 1 separation occurs at an altitude of 109 Kilometers and a velocity of 4,547m/s. At that point, the stack enters a 100-second coast period to get close to apogee for the second stage burn. After 100 seconds of coasting, the Payload Fairing is jettisoned at an altitude of 184 Kilometers. Ten seconds later, the second stage begins its engine burn for orbital insertion and circularization. Stage 2 shutdown occurs about 471 seconds into the flight at an altitude of 205 Kilometers and a velocity of 7,521m/s. Payload separation occurs after 120 seconds of maneuvering by the second stage attitude control system. The typical Cygnus insertion orbit is 275 by 250 Kilometers at an inclination of 51.66 degrees. (emphasis added)
Question: What are the orbital-mechanical advantages of a long (100+ second) sub-orbital coast phase between first and second stage burns in some cases? It's pretty rare for a multi-stage launch to LEO to do this.
If possible, a little math showing how this helps would be great!