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A simple analytical equation to calculate the atmospheric drag during aerobraking campaigns. Application to Mars. François Forget & Michel Capderou Laboratoire de Météorologie Dynamique, CNRS 14/12/2010. Atmospheric drag and velocity change Δ v during an orbital pass through the atmosphere .

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A simple analytical equation to calculate the atmospheric drag during aerobraking campaigns. Application to Mars.

François Forget & Michel Capderou

Laboratoire de Météorologie Dynamique, CNRS

14/12/2010

coupling an orbitography numerical model and an atmospheric model here
Coupling an orbitography numerical model and an atmospheric model. Here:

Mars Climate database

(Forget et al. 2006)

Ixion orbitography

(Capderou 2005)

http://climserv.ipsl.polytechnique.fr/ixion.html

“Mars aerobraking simulator”

example delta v during a 200 sols 1314 orbits drag compensated aerobraking campaign
Example : Delta V during a 200 sols (1314 orbits) “drag compensated” aerobraking campaign
  • - MGS like shape
  • - Inclination = 75°
  • - Excentricity = 0.4
  • - Initial conditions:
  • Ls=0°
  • Periapsis at 0°N,
  • z=100km

Can we calculate Delta V without having to run complex models for quick look estimation and mission strategy design ?

previous analytical work very complex equations by king hele 1987 on the contractions of orbit
Previous analytical work: very complex equations by King-Hele (1987) on the “contractions of orbit”
calculation of aerobraking v over one orbit
Calculation of aerobraking Δv over one orbit
  • Drag force on spacecraft:
  • Change of velocity a time t:
  • Integration over one orbit (period T ) :
slide7

v2

ρ

calculation of aerobraking v over one orbit 2
Calculation of aerobraking Δv over one orbit (2)
  • Assuming that around perihelion the atmosphere is relatively isothermal (scale height H) :
  • Integration of one orbit (period T ) :
  • Playing with the Keplerian equations (with simplification and development around periaspis) give the variation of altitude as function of time:
slide9

Relative velocity at perisapsis

Scale height at periapsis (RT/g)

Density at perisapsis

validation delta v during a 200 sols 1314 orbits drag compensated aerobraking campaign
Validation : Delta V during a 200 sols (1314 orbits) “drag compensated” aerobraking campaign
  • - MGS like shape
  • - Inclination = 75°
  • - Excentricity = 0.4
  • - Initial conditions:
  • Ls=0°
  • Periapsis at 0°N,
  • z=100km
validation delta v during a 200 sols 1314 orbits drag compensated aerobraking campaign1
Validation : Delta V during a 200 sols (1314 orbits) “drag compensated” aerobraking campaign
  • - MGS like shape
  • - Inclination = 75°
  • - Excentricity = 0.4
  • - Initial conditions:
  • Ls=0°
  • Periapsis at 0°N,
  • z=100km
statistics of errors simple equation reference model over one mars year simulations
Statistics of errors (simple equation – reference model) over one Mars year simulations

Orbit Inclination:

impact of the relative wind
Impact of the relative wind
  • One must take into account the motion of the atmosphere in addition to the spacecraft velocityVspc.
  • Notice that the transverse component Vt is always negligible, unlike the axial component Va, because V02 ~ (Vspc+Va)2 >> Vt2

Atmospheric motion Vt

(transverse component, galilean frame)

Spacecraft velocity Vspc

(Galilean frame)

Atmospheric wind Va

(axial component)

estimation of the relative wind
Estimation of the relative wind
  • Case 1 : spacecraft velocity and atmospheric wind known from models:
  • Case 2: neglect planet rotation and winds
  • (use only spacecraft velocity in galilean frame)
  • Case 3: atmosphere rotating like the solid planet
conclusions and perpectives
Conclusions and perpectives
  • Velocity change Δv during an orbital pass through the atmosphere can be computed using a simple equation with error < ~5% (better than error on density…)
  • e.g. :
  • This should be useful for preliminary mission design by non specialists, simple scaling,to develop autonomous aerobraking system, etc…
  • Conversely, estimation of the velocity change provide an estimation of density at periapsis in real time.
  • This equation should be valid on other planets