I tried to do this problem for about an hour and I'm getting a little frustrated ... am I just overthinking it?
The International Space Station requires two types of propulsion systems for its operation. The first is to re-boost the station to the correct orbital altitude (to offset the effects of atmospheric and other drag forces) and to maneuver the ISS to avoid collision with other orbiting bodies (i.e., debris). The other is attitude control to position the station in the proper attitude for various experiments, temperature control, re-boost maneuvers, etc.
The ISS has been in space since November 1998. It needs frequent re-boosts as the friction in the ultra-thin atmosphere and gravity are dragging the ISS slowly back to Earth.
Calculate how much fuel will be used if the ISS needs a re-boost and is 85% through its construction phase. The orbit of the ISS is at 325 kilometers and you need to re-boost the station to a 350 kilometer orbit.
Use the equation, F=Ma (Force=Mass*acceleration) to determine the length of the burn needed to lift the ISS to its desired altitude. The delta-V (change) needed to make this orbital maneuver is precisely 23.4696 meters per second (m/s).
The station weighs approximately 277,598 kilograms. The combined thrust of the Progress engines that will perform the re-boost is 823.8Newtons (force). Your answer will be in meters per second squared (m/s/s).
Hint: First find the acceleration and then take the required delta-V and divide it by the acceleration, in order to get the burn time. To determine the amount of fuel used, multiply by the fuel flow rate of the Progress engines, which is .307 kilograms per second (kg/s).