The general thrust equation for rockets is: F=mdot*V_{e} + (P_{e} - P_{a})*A_{e} where, F=thrust, mdot=mass flow rate, V_{e}=velocity of the exhaust at the nozzle exit, P_{e}=exhaust pressure at the nozzle exit, P_{a}=ambient pressure, and A_{e}=area of the nozzle exit.When considering the P_{a} term during the low altitude segment of the flight, is that very strictly the general atmospheric pressure at the rocket's altitude? I believe the forward travel of the rocket and backward travel of the high velocity exhaust gasses creates a localized low pressure at the base of the rocket (this causes the plume recirculation seen on some launches, right?). Does this area's lowered pressure need to be taken into account for a higher accuracy calculation of the thrust?

If nozzles point directly backward, then variations in thrust of one engine with respect to another will tend to make the rocket turn a bit. That is eliminated if each engine's thrust vector points at the rocket's center of mass.

This post isn’t really meant to answer the gravity losses question but rather summarize my understanding of what gravity losses are. So if I’ve got something wrong please point it out. Orbit isn’t about altitude per se but rather velocity. You need an angular velocity such that the centrifugal force is equal to the pull of gravity to essentially nullify it and enter orbit. Given that we have an atmosphere on earth, achieving the required velocity is easier/possible if your altitude places you outside or at least in the very very thinnest parts of the atmosphere. In order to achieve that altitude, you have to spend some of your fuel countering gravity to increase altitude rather than devoting all the fuel to increasing tangential velocity, thus you lose something to gravity. If you had a perfectly spherical body with no atmosphere you could orbit just off the surface given you have the necessary angular velocity, and orbit could be achieved with almost no gravity losses. Is that at least a decent conceptualization of gravity losses? If I’m understanding the concept correctly the launch trajectory would affect the amount of gravity losses that occur. A more lofted trajectory would have greater losses versus one that pitches down range earlier in the ascent. But there is a sweet spot between fighting atmospheric drag versus gravity losses that would define the “ideal” trajectory. Different trajectories from the ideal might be chosen for various reasons (such as?). What other factors in rocket design and launch trajectories affect gravity losses. I appreciate the feedback and the tremendous resource NSF is for us amateur armchair rocketeers and space nerds.