Editing Spacecraft flight dynamics (section)

===Propulsion===

The thrust of a [[rocket engine]], in the general case of operation in an atmosphere, is approximated by:<ref name="Sutton">{{cite book|author=George P. Sutton|author2=Oscar Biblarz|name-list-style=amp|title=Rocket Propulsion Elements|edition=7th|publisher=Wiley Interscience|date=2001|isbn=0-471-32642-9}} See Equation 2-14.</ref>

<math display="block">F = \dot{m}\;v_{e} = \dot{m}\;v_\text{e-opt} + A_{e}(p_{e} - p_\text{amb})</math>
where,
*<math>\dot{m}</math> is the exhaust gas mass flow
*<math>v_{e}</math> is the effective exhaust velocity (sometimes otherwise denoted as ''c'' in publications)
*<math>v_\text{e-opt}</math> is the effective jet velocity when ''p''<sub>amb</sub> = ''p''<sub>e</sub>
*<math>A_{e}</math> is the flow area at nozzle exit plane (or the plane where the jet leaves the nozzle if separated flow)
*<math>p_{e}</math> is the static pressure at nozzle exit plane
*<math>p_\text{amb}</math> is the ambient (or atmospheric) pressure

The effective exhaust velocity of the rocket propellant is proportional to the vacuum [[specific impulse]] and affected by the atmospheric pressure:<ref name="RPE7">{{cite book|first1=George P.|last1=Sutton|first2=Oscar|last2=Biblarz|title=Rocket Propulsion Elements|url=https://books.google.com/books?id=LQbDOxg3XZcC|publisher=John Wiley & Sons|date=2001|isbn=978-0-471-32642-7|access-date=28 May 2016|url-status=live|archive-url=https://web.archive.org/web/20140112033956/http://books.google.com/books?id=LQbDOxg3XZcC | archive-date=12 January 2014}}</ref>
<math display="block">v_e = g_0 \left(I_\text{sp-vac} - \frac{A_{e}\, p_\text{amb}}{\dot{m}}\right) </math>

where:
*<math>I_\text{sp-vac}</math> has units of seconds
*<math>g_0</math> is the gravitational acceleration at the surface of the Earth

The specific impulse relates the [[delta-v]] capacity to the quantity of propellant consumed according to the [[Tsiolkovsky rocket equation]]:<ref>{{cite book|author=George P. Sutton|author2=Oscar Biblarz|name-list-style=amp|title=Rocket Propulsion Elements| edition=7th| publisher=Wiley Interscience|date=2001|isbn=0-471-32642-9}} See Equation 3-33.</ref>
<math display="block">\Delta v\ = v_e \ln \frac {m_0} {m_1}</math>
where:
*<math>m_0</math> is the initial total mass, including propellant, in kg (or lb)
*<math>m_1</math> is the final total mass in kg (or lb)
*<math>v_e</math> is the effective exhaust velocity in m/s (or ft/s)
*<math>\Delta v </math> is the delta-v in m/s (or ft/s)