How Does the Jacchia Model Predict Atmospheric Drag for Satellites in LEO?

[Astronuc]

The subject was part of a presentation today on orbital determination and orbital mechanics. Lots of variables to consider, but in particular for satellites in LEO, how much drag occurs in the atmosphere, and how does it vary peridically (day/night during an orbital period), seasonally (as the earth moves around the sun), and with the solar cycle?

https://en.wikipedia.org/wiki/Jacchia_Reference_Atmosphere

Original papers -
https://articles.adsabs.harvard.edu/full/1964SAOSR.170.....J
https://adsabs.harvard.edu/full/1971saosr.332.....j

https://ntrs.nasa.gov/api/citations/19830012203/downloads/19830012203.pdf

https://ai-solutions.com/_help_Files/jacchia_roberts_density_model.htm

https://www.mathworks.com/matlabcentral/fileexchange/56163-jacchia-bowman-atmospheric-density-model
https://www.mathworks.com/matlabcentral/fileexchange/54921-modified-jacchia-70

The Jacchia Reference Atmosphere is an atmospheric model that define values for atmospheric temperature, density, pressure and other properties at altitudes from 90 to 2500 km. Unlike the more common US Standard Atmosphere and related models, the Jacchia model includes latitudinal, seasonal, geomagnetic, and solar effects, but must be supplemented with another model at lower altitudes. The model, first published in 1970 and updated in 1971 and 1977, is based on spacecraft drag data, and is primarily used in spacecraft modeling and related fields. A common assumption while using the Jacchia Model is that the atmosphere rotates with the Earth as a rigid body.

Ref: Meysam Mahooti


https://ui.adsabs.harvard.edu/abs/1983CeMec..29....3D/abstract

 

[D H]

How Does the Jacchia Model Predict Atmospheric Drag for Satellites in LEO?

I'll get to this question a bit later, but first I'll write about upper atmosphere models.

The Jacchia model is "simple" (it's rather complex, but compared to other upper atmosphere models it is "simple"). It is also outdated as it was last updated in 1977. It does however live on in multiple forms such as the Jacchia-Bowman model (released in 2006, updated in 2008), the Marshall Engineering Thermosphere model (updated many times), the Earth General Reference Atmosphere Model (Earth-GRAM), updated many times.

A very good alternative to Jacchia-based models (arguably much better than Jacchia) is the family of Mass Spectrometer and Incoherent Scatter (MSIS) models. These date back to the early 1960s, and have been regularly updated. The NRLMSISE-00 (Naval Research Laboratory MSIS Extended, released in 2000) has become the gold standard of upper atmosphere models. It has been updated twice since 2000, but the license agreement on later releases is horrendous. Those updates cannot be used for commercial software -- or for commercial spacecraft. The NRLMSISE-00 has no license agreement, which is almost as bad as the horrendous agreement in later releases.

The NRLMSISE-00 is a part of the Committee On Space Research (COSPAR) International Reference Atmosphere (CIRA) , along with a wind model (the Horizontal Wind Model (HWM07)), augmented with the Alaska Volcano Observatory Ground to Space (AVO-G2S) model.

Inputs to any of these models include (not a complete list)

• Altitude, latitude and longitude, because the atmosphere varies with position,
• Local apparent time of day because the upper atmosphere has a diurnal bulge,
• Day of year because the upper atmosphere undergoes annual latitudinal fluctuations,
• Solar activity, using F10.7 measurements as a proxy, because one little puff from the Sun can make the upper atmosphere swell immensely.

Whether a wind model is needed for modeling drag on an orbiting spacecraft is dubious. A 1000 kph wind (not very likely!) is next to nothing compared to the 7.8 km/s orbital velocity, particularly since the density estimations can easily be off by several percent. Wind models are needed for launches; NASA and others typically release balloon sondes (and sometimes, rocket sondes) prior to launch to detect winds and how they change with altitude. Too much sheer can cancel a launch, and lesser sheer can move launch vehicles off course unless compensated for.

Now to the main question: How Does the Jacchia Model Predict Atmospheric Drag for Satellites in LEO?

It doesn't, at least not directly. The above atmosphere models describes how the atmosphere behaves. To predict drag, one also needs a model of how the spacecraft interacts with the atmosphere. Two options are available, one very simple and the other very complex.

The simple model is a coefficient of drag model (or equivalently, a ballistic coefficient model). All one needs is the drag coefficient, the cross section area to the atmosphere, the atmospheric density, and the spacecraft's velocity relative to the atmosphere. To make matters even easier, the coefficient of drag is typically assumed to be 2.2 (compare with a very good parachute, which has a C_d of 1.5). Shape is rather irrelevant in space; all shapes are not very aerodynamic in space. So now all one needs are atmospheric density and cross section area. The general assumption for this simple C_d-based model is that the spacecraft is flying in the desired orientation, so cross section area is a known quantity. The atmosphere model provides the density.

The much more complex model is to use a flat plate CAD model of the spacecraft. Each plate can interact with the atmosphere that depend on whether other parts of the spacecraft are shielding the plate in question from the atmosphere and that depend on how atmospheric particles interact with the plate. The former (shielding) is important due to the very long mean free path of particles in the upper atmosphere. The latter (interactions) include specular reflections, diffuse reflections, and (temporary) sticking. This can be hideously complex and typically is not something someone should attempt to do in a realtime (or faster) simulation. An intermediate level model is to use a time-varying cross section to drag, calculated ahead of time using a computational fluid dynamics model based on predicted orientation.

I'll add references, but this will happen later.