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# Delta V calculator for LEO/MEO/GEO orbit injection

 Transfer orbit inclination (or launch site latitude) Initial circular orbit height, same as transfer orbit perigee altitude (bottom) Transfer orbit apogee altitude (top) deg km km

 Initial, circular, low earth orbit Velocity m/s Injection into elliptical transfer orbit delta V m/s Injection into circular orbit delta V (inc+circ) m/s Final circular orbit Velocity m/s Final orbit period hours Final orbit geo drift rate deg/day

 Low earth orbit mass (inc fuel) Specific Impulse of perigee thruster kg s
 Fuel used at perigee injection kg Transfer orbit Mass kg

 Transfer orbit mass Specific Impulse of apogee thruster kg s
 Fuel used at geo injection kg Beginning of Life GEO Mass kg

Enter your initial low earth circular orbit inclination and height.

Example inclinations: Based on latitudes of launch sites:
Sea Launch 0 deg, Kourou 5.23 deg, Kennedy 28.5 deg, Tyuratam 46 deg.

Example initial low parking orbit heights: 200 km or 300 km.

Final circular orbit height for geostationary orbit satellites is 35786.13 km
O3b orbit height is medium earth orbit (MEO) at 8063km.

If interested, enter your low earth circular orbit  'off-the-rocket' orbit mass (inclusive of spacecraft fuel) and specific impulse of the perigee motor.
Specific impulse of solid fuel motors is about 285 to 295 s.
Liquid bi-propellant systems give a specific impulse of about 310 s.
Ion thrusters, specific impulse = 1000 - 10000 s (approx)

Calculation results are the delta Vs to get from circular LEO orbit to elliptical transfer orbit and and from transfer orbit to geo orbit and fuel used.

Notes:

These are approximate calculations.  Typical launch sequences may involve direct injection into a transfer orbit with probably a small reduction of the inclination at the same time.  The calculations assume impulse (short time) burns so that the spacecraft does not move significantly during the burn time.  If it takes longer you would do better to split the burn into a sequence of shorter burns done at the sequential apogees (about 12 hours apart).  You may wish to start the orbit life with a small 'negative' inclination so it settles down of its own accord by the time you want to commence service. Ion thrusters have very high specific impulse but very low thrust so are better suited to station keeping rather than transfer orbit manoeuvres. If used for GEO orbit injection the use of ion thrusters give a very substantial reduction in cost to GEO orbit, but at the penalty of a very long time taken to get there.  A typical apogee motor with have a thrust of 490 N, while an ion thruster will have a thrust of 0.05 N, so it might take perhaps seven to ten months to raise the orbit using ion thruster.

17 Sept 2015: Modified to allow the possibility of using different specific impulses for transfer orbit and geo injection, illustrating the benefit of ion thrusters, albeit with the very long thrusting times, measured in months.

This calculator is only for educational purposes.  The results of may be in error and should not be used for orbital manoeuvres or the navigation of real spacecraft.

If anyone uses this page and is able to do the calculations independently themselves please tell me where I am wrong.