Once a rocket is in orbit, if it needs to change it's orbit (either from a lower to a higher orbit, or from a circular to an elliptical orbit), it needs to execute an Orbital Maneuver. This is accomplished by using a small impulse from thrusters to change the tangential velocity, and hence slip into a different orbit as a consequence.
Types of Orbital Maneuvers
figures showing a) Hohmann transfer and b) Bi-elliptic transfer
The Oberth Effect
The Oberth Effect is interesting: roughly what it states is that A rocket will gain more velocity while firing it's engines at a higher velocity than by firing them at a lower velocity. This is because the fuel has kinetic energy by virtue of the rocket's motion, and travelling at higher velocity = more kinetic energy in the fuel that the engines convert to exhaust gases.
This effect can be used in a gravitational slingshot, when at the periapsis (closest point) of an elliptical orbit, a burn is more effective and gives you higher velocity gain as compared to burning as you're entering the gravitational well.
Note that this is only applicable to reaction engines: it's less effective for something such as an Ion Engine
My father is an aerospace engineer by training, and this popped up in one of our long conversations about life (I've recently returned home, so enjoying these moments). In somewhat of a continuation to the World is a Universe, and Life is your Trajectory idea, this rocket took off when I got into IIT Delhi, and the second (third?) stage burn gave me my Department Change. I'm peacefully in one orbit now, but over the next two years, I'd have to prepare for the next orbit change: my internship, followed by applications for Masters and/or Placements. As a result, a majority of my efforts would lie in timing and firing the burn required for this orbital maneuver, rather than finding the path of least resistance in my current orbit (which I believe I've already done in the past year).
Staying healthy, focused, and motivated would be the primary goal for the next two years, while slowly detatching from other college-centric and people-focused activities and focusing more on the future and my skills.
PS: a lot of new articles have a more personal flavour to them, courtesy me having my professional and this webpage separate, and also as a consequence of being inspired by a friend's blog. Let's see how long I stick with it :)