Thinking Map of Kepler's Elements by Carlos Alvarado

Orbit

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-a closed path around which a satellite travels, ellispses

Eccentricity (e)

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describes the roundness
a- semi major axis
b-semi minor axis
when (e)=0, orbit is circular
when (e) approaches 1 orbit is highly elliptical
all closed orbits are 0(e) is always between 0 and 1 for any closed orbit

Keplerian Elements

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Two describe the shape and size of the orbit
three describe the the orientation of the orbit in space
One describes the location of the satellite within the orbit
plus a time stamp

Semi-Major Axis

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(a)-describes the size of the ellipse
- half of the largest diameter
- originates from the, not necessarily where the central body is
Apogee- orbit point farthest from the earth
Perigee-orbit point closest from the earth
In a circle apogee and perigee are the same so both are undefined
Earth Radius- 6,378 km
The only parameter that determines period(T)
Gravitational Constant = 6.67x10^-11m^3/kg*s^2
Mass of Central Body (Earth)-M-5.98x10^24kg
PI=3.14
Only parameter that determines period (T)

Inclination (i)

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angle between earth's equatorial place and the plane of the orbit describes the tilt (pitch)
Measure in degrees
i-0º is is called equatorial orbit
i-90º is called polar orbit

Ground Trace

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given ground chase , period and inclination can be found
top or bottom degree= inclination
the trace gap - way to determine the orbit period
4 mins per degree
gap degrees *4 =period (T)

Right Ascension of the ascending node

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RAAN , Omega
the rotation or twist about the earth (yaw)
angle measured along equatorial point in space (vernal equinox) and the point where the motion is from south to north across the equator (ascending node)
measured in degrees
ascending - from south to north (up)
Omega-0 when ascending node is aligned with vernal equinox

Argument of Perigee (w)

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describes the orientation of the apogee and the perigee (roll)
angle from the ascending node to the perigee point
measure in degrees 0only exist if perigee exists

True anomaly (v)

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once orbit is completely described satellite's location on that orbit measured in degrees
perigee=0º
apogee=180º
measured in the direction the satellite moves

Epoch(time stamp)

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describes WHEN the set of values accurate for the satellite (snapshot)

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1st Law

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satellites travel around the earth in an elliptical path Earth at a foci

3rd Law

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Orbital Period (T) is related to its semi major axis

2nd Law

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The line sweep from earth to a satellite will be equal areas during equal time periods anywhere on the orbit path.