Orbital Mechanics Calculator

Orbital velocity and period are an integral part of space mission design that is affected by key parameters such as the apogee and perigee of the spacecraft's orbit. This orbital mechanics calculator can help you the orbital velocity and period of a spacecraft in any circular or elliptical orbit around the Earth.
CalculationInputs﻿﻿Apogee Height
:700.00km​
﻿
﻿﻿Perigee Height
:700.00km​
﻿
Constants
﻿﻿Radius of Earth
:6378.1km​
﻿
﻿﻿Gravitational Parameter of Earth
:398600m3/s2​
﻿
﻿
Primary outputs﻿﻿Orbital Velocity (Apogee)
:7.50km/s​
﻿
﻿﻿Orbital Velocity (Perigee)
:7.50km/s​
﻿
﻿﻿Orbital Period
:1.65hours​
﻿
﻿﻿Eccentricity
:0.0​
﻿
Explanation
﻿
Perigee and apogee explanation
Perigee and apogee are terms used in orbital mechanics to describe the closest and farthest points, respectively, between an object and the primary body it orbits. Perigee represents the point of closest proximity, while apogee denotes the farthest distance in the object's orbit.
Additional equations and outputsThe radii of the apogee and the perigee of the orbit is found using:
﻿
R=RE+AR = R_E + AR=RE​+A
﻿
R=Radius of Apogee/Perigee (km)RE=Radius of Earth (km)A=Altitude of Apogee/Perigee (km)R = Radius\,of\,Apogee/Perigee\,(km)\\R_E=Radius\,of\,Earth\,(km)\\A = Altitude\,of\,Apogee/Perigee\,(km)\\R=RadiusofApogee/Perigee(km)RE​=RadiusofEarth(km)A=AltitudeofApogee/Perigee(km)
﻿
﻿﻿RA
:7,078.10km​
﻿
﻿﻿RP
:7,078.10km​
﻿
The semi-major axis of the orbit is found using:
﻿
SMA=RA+RP2SMA=\frac{R_A+R_P}{2}SMA=2RA​+RP​​
Where:
﻿
SMA=Semi−Major Axis (km)SMA=Semi-Major\,Axis\,(km)SMA=Semi−MajorAxis(km)
﻿
﻿﻿SMA
:7,078.10km​
﻿
The specific energy of the spacecraft in orbit is found using:
﻿
ϵ=−GP2∗SMA (km2/s2)\epsilon=-\frac{GP}{2*SMA}\,(km^2/s^2)ϵ=−2∗SMAGP​(km2/s2)
Where:
﻿
ϵ=specific  energy  (km2/s3)GP=Gravitational  Parameter\epsilon = specific \: \:energy \: \:   (km^2/s^3) \\ GP=Gravitational \: \: Parameterϵ=specificenergy(km2/s3)GP=GravitationalParameter
﻿﻿Specific energy (km2/s2)
:-28.16​
﻿
﻿
The orbital velocity of the spacecraft at any point in the orbit is found using:
﻿
vorbital=2∗(GPR+ϵ)  (km/s)v_{orbital}=\sqrt{2*(\frac{GP}{R}+\epsilon)} \,\,(km/s)vorbital​=2∗(RGP​+ϵ)​(km/s)
﻿﻿Orbital Velocity (Apogee)
:7.50​
﻿
﻿﻿Orbital Velocity (Perigee)
:7.50​
﻿
The orbital period in hours of the spacecraft is found using:
﻿
T=2π(SMA3GP)13600  (Hours)T =2\pi (\sqrt{\frac{SMA^3}{GP}})\frac{1}{3600} \,\,(Hours)T=2π(GPSMA3​​)36001​(Hours)
﻿﻿Orbital Period
:1.65hours​
﻿
﻿
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