“Raavana-1” Orbital Decay Analysis and Re-entry Prediction

Sadeepa Sepala (4S6SAD)

26th Sep 2021

Summery:  The  Raavana-1  cube satellite s orbit  is decaying rapidly  

and it will re-enter earths atmosphere  on or around 7 th Oct 2021

Introduction

“Raavana – 1” is the first ever Sri Lankan low earth orbit (LEO) cube satellite launched in to orbit. Mr Tharindu Dayarathna, Ms Dulani Vithanage and Mr Kavendra Sampath from Arthur C Clark Center for Modern Technologies  designed, built and operated it. It was deployed in to orbit from ISS on 17th June 2019. Soon after lunch, it started to transmit telemetry/image data and involved in doing experiments on LoRA and earths magnetic field, sparking great enthusiasm about space technologies in local community. 

After successful operation of more than  2 years Raavana-1’s orbit has started to decay rapidly signing its reaching end of life soon. The increased solar activity seems to have accelerated the decay by increased atmospheric drag. Following sections analyses the orbital decay based on parameters derived from historical TLE data from https://www.space-track.org/ and other online sources. Finally it is attempted to predict on re-entry based on decay data with simple empirical polynomial approximation.

Orbital analysis

The Two Line Elements (TLE) are very popular way of distributing orbital elements of any earth orbiting object (some times refereed to as ‘Keplers’ since these data contain the classical Keplarian orbital elements). These TLE data are mainly used by satellite tracking application s to calculate visibility of satellites at particular location. TLE data for almost all satellites orbiting earth are publicly available form any online sources. Example TLE data for Raavana-1 is as follows.

Raavana-1

1 44329U 98067QE  19181.69100881  .00004104  00000-0  74322-4 0  9996

2 44329  51.6417 294.2032 0007660 126.9896 233.1796 15.52083104  2125

For orbital analysis of Raavana-1, TLE data for each day from 18th June 2019 to 25th Sep 2021 were obtained from space-track.org. Then a python script is developed to extract orbital elements and to calculate some derived parameters. 

  Fig 1 : Orbital elements - [image source : 

https://www.wikiwand.com/en/Orbital_elements ]

Basic Newtons, Keplers laws and geometrical properties of eclipses are used in calculating derived parameters.

Let

Semi Major axis = α km

Mean Motion = n rev/day

Apoapsis = Ra km ( Furthest distance from earth )

Periapsis = Rp km ( Closest distance from earth )

Eccentricity = e

Then 

α = μ1/3 / [2nπ / 86400]2/3     ;   Ra = α (1+e)   ;   Rp = α(1-e)  

where μ = standard gravitational parameter for earth ( G.Me ) = 3.986004418×1014       m3s−2

Raavana-1 does not have its own population system and in low earth orbit, therefore its orbit gradually decays over time mainly due to drag from residual gasses in upper atmosphere and gravitational perturbations of from celestial bodies. The atmospheric drag rapidly increases as satellite reaches lower in to denser regions of the upper atmosphere. 

Raavana-1 was deployed from ISS, and therefore its initial orbit was about 423km height over earth. From Fig 3, by April 2021 its orbit got decayed almost linearly down to 350km (83% of original height). 

Afterwards it has started to experience more and more drag and its orbit has started to decay exponentially. As of 25th Sep 2021 TLE data, its periapsis (closest distance to earth) is 250 km, that is just 59% of the original height. Rate of periapsis decay is also calculated by numerical differentiation (backwards differences method) of periapsis with respect to epoch and smoothed with moving average. Fig-4 shows the resultant plot which clearly shows the exponential growth of decay rate.

Below 350km the atmospheric drag becomes more significant than the gravitational forces. Therefore the drag is more related to the density of the atmosphere. Actually this region of atmosphere also known as ionosphere the density is inversely related to height and greatly influenced by solar activity. Fig-5 and Fig-6 shows the close correlation of drag and 1st derivative of meam motion with with recent solar and geomagnetic activity.

Re-Entry Prediction

Modeling and prediction of re-entry of a cube sat is extremely complex problem due to its high dynamic nature. Mainly this includes modeling the drag forces and solving an aerothermodynamic problem in supersonic speeds. The satellites acceleration due drag forces acting upon can be roughly modeled as 

 

   adrag= - ½ Cd (A/m) ρv2   

Where Cd = Drag coefficient (model), ρ – Atmospheric density (model), m – mass of the satellite, A – satellite surface perpendicular to speed (ram area), v – satellite speed wrt atmosphere

Therefore many of the parameters are highly dynamic in nature and difficult to predict accurately. Atmospheric density it self is dependent on many factors and complex models are developed by NASA and other researchers, which includes Solar flux number. Fig-7 shows the graphical representation of such model for solar max and solar min.

All other parameters of the above deceleration model related to satellites attitude and physical attributes like surface area , inertia etc ..(Fig-8). Therefore by studying already re-entered satellites of similar properties should give greater insights in to the re-entry model.

Prior to Raavana-1, three similar satellites namely UITMSAT-1, MAYA-1, BHUTAN-1 (Birds-2) were launched to approximately the same orbit. Those satellites have re-entered earths atmosphere  around 20th Nov 2020 and their orbital data were analyzed similar to the above approach. From those data it was found that orbital heights of last 100 day or so could be approximated by 6th to 8th degree polynomial and all those satellites have re-entered earths atmosphere altitude of around 170km.

Therefore Raavana-1’s orbital height (perigee height) is approximated by 6th degree polynomial using curve fitting techniques readily available in spreadsheets and arrived on reentry date of 7th OCT 2021. This date is just a crude estimate and by no means this is the final date. It would be heavily dependent on solar activity (There is a predicted Geomagnetic storm of class G2 on 26-27 Sep, which may have significant impact on re-entry date).