Journey of Aditya L1 spacecraft to Halo Orbit around Earth-Sun Langrange1 point

 

ISRO has launched a Spacecraft ADITYA_L1 to study Solar phenomenon on 2nd September 2023. It will be placed in 'HALO' orbit around Langrange Point 1.

As one can see, words like      HALO,       Lagrange Point1,     are alien to common folks so first we will try to understand them starting with elementary school knowledge of Magnetism.

Figure shows how he undisturbed magnetic field of Earth ( shown in the leftmost part ) gets disturbed with a bar magnet.

 Two cases are
1. With North pole of bar magnet pointing to Geographic North and
2. South Pole of bar magnet pointing to Geographic North.

We know that we get two NULL points in each case , two points are perpendicular to magnet axis in first case  and in 2nd case these points are along the axis of magnet.

A somewhat similar situation creates what are called as Lagrange points  ( 5 points  ..  similar to 2 nulls in case of bar magnet ).

But we will concentrate on only one of them called Lagrange1 ( L1, for short ) point, which is a Null point between Sun-Earth line, at a distance of about 1.5Million kms from Earth towards Sun.

( For those who want to know more about these points , read here )

Since both Earth and Sun gravitational pulls are equal a satellite kept at that point will remain there but prone to loose its stability and fall to any one side: Either as a satellite of Earth or a satellite of Sun like any planet. 

With a clever manipulation of insertion point direction the satellite can be forcibly made to 'revolve' around L1 point in a small orbit using the gravities of both Sun and Earth. Remember that there is no 'real' central mass around which this orbit is revolving. The orbit is formed due to a precarious dynamic balance of gravitational pull by both Sun and Earth and the kinetic energy of orbiting body.

With this knowledge of L1 and Halo we move further now with a specific focus on ADITYA L1 orbit and how it is achieved. ( We will use ADI to mean ADITYA_L1. )

On 2nd Sept 2023, ISRO launched  ADI atop PSLV C57 rocket and at the end of the flight, ADI achieved 233 Kms X 19470 Kms orbit. 

With the capability of PSLV, maximum velocity that could be provided to ADI was about 9.7 kms/sec. 

To break Earth's gravity the escape velocity is 11.2 km/sec. 

This velocity increase was achieved by successive increase of Apogee by firing thrusters at Perigee and this procss of Orbit raising is called Earth Bound Maneuvers numbered EBN#1, EBN#2,EBN#3 and EBN#4.

  List of EBNs and orbits ( Perigee Height X Apogee Height )  achieved after each:

1. Launch orbit : 233Km X 19470 Km     (  Sept 2 )

2. After EBN#1 :  245 Km X 22459 Km  ( Sept 3 )

3. After EBN#2 :  282 Km X 40225 Km  ( Sept 5 )

4.  After EBN#3 :  296 Km X 71767 Km  ( Sept 10 )

5.  After EBN#4: 256 Km X 121973Km   ( Sept 15 )

Other operations carried out on  ADI :

1. Sept 30 : ADI escapes SoI of Earth's gravity; 

2. Oct 8 : Trajectory Correction Maneuver ( TCM ) done to precisely bring the Spacecraft to its planned trajectory.

3. Nov 7 : HEL1OS equipment starts working and captures a Solar flair.

4. Around 7th January 2024 a Halo Orbit Insertion Maneuver may be carried out by ISRO.

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ADI  path to its HOME orbit around Lagrange1 point

Figure on below shows the path ( White Trajectory ) of ADI from Launch ( 2nd Sept 2023 to 17th March 2024 ) as published by ISRO on NASA's Horizons website. Earth is at the intersection of axes. ADI started its journey from near the origin.

The BLUE ( Z ) axis is Celetial North South axis passing through the centre of Earth. RED ( X ) axis is the Equinoxes joining line ( Also the line on which Equator and Ecliptic cut each other. ), Y axis is orthogonal to X and Z axes. 

 Initial orbit raising raised the orbit and after final EBN#4, it started its journey almost parellel to -X direction i.e. towards L1 location.

For clarity we remove axes in next figure on Left, and color the ADI path pink and mark various events as they happen on the way. We also add the path of L1 around Earth as it rotates around Sun.

Figure on Right above shows Same situation but from little South and add corresponding time tags on L1 path ( Green ) also which allows us to imagine the relative position of ADI and L1 at a monthly interval.

We notice that ( we are not using scientific terms, but just relative description ) 

1. at SoI point the ADI is south of L1 and it travels northwards 

2. Around 1st Dec it crosses over to south of L1 path BUT, it is almost farthest Left of L1.

3.  Slowly ADI comes nearer to L1 and on 7th Jan it is nearest to L1. 

4. As time passes, around mid February,  ADI crosses over from South to North of L1 path. However, again both are farthest from each other and ADI is Right of L1.

It is difficult to visualise the path of ADI    w r t    L1.  

For that we attempt to continuously rotate our xyz axes so that L1 ( and the Sun behind it ) are always pointing to the  '-x'  direction of new xyz frame. 

( Let me confess : For the FIRST time in my life I found that one of the 1st theorem I had learnt in Co-ordinate geometry   viz. Rotation of axes has a utility factor..   otherwise like many other things I was assuming it to be a useless learning in school/college !! )

After we apply that ( Rotation angle as a function of Time difference at every point ), Viola,  we get the following :

In this figure Sun is away from viewer along -X direction ( Red axis ) and L1 ( Green dot ) is on the line joining Earth ( 0,0,0 ) and Sun.    We hide axes and initial travel of ADI upto SoI exit point.

  Before we explore further this elliptical orbit, a small clarity. 

Lets look to the path from  side... ( as seen in Right image above )

We can clearly see a small but sure change in the path midway from SoI exit and Ecliptic crossing..  That is where around 7th Jan2024, ISRO will insert the ADI into its intended Halo orbit.

So what you see on upper portion in this figure is its journey to the intended orbit and from that point onwards is a part of the actual Halo orbit.

 

 We redraw the Halo Orbit  ( from Left image above ) path in two parts:

1. Before Halo insertion point ( Green portion ) and   2. After Halo insertion ( Pink portion ),

and superimpose the theoretical complete Halo orbit. ( Dashed Pink in lower image ) over it.

Apparently this looks to be a simple elliptical orbit ...   B U T  it is a highly deceiving shape when we see it in 3 dimension.

 

Let's add the axes frame with, 

Earth at origin ( 0,0,0 ) and 

X axis aligned with SUN-EARTH line ( Sun in -X direction ) and 

Z axis to Celestial North.

Lagrange1 point is -1.5 Million Kms on X axis and Sun is at -1AU from Earth.

 Let's look to Halo orbit from 3 orthogonal positions shown by arrows in Right above figure. 

The same Halo orbit looks different from 3 directions as shown in the figure below

           The reason why we see 3 shapes is that the Halo orbit is NOT a FLAT ellipse but is a 3 dimensional figure like a Shell. Especially the curvature in view along Y axis is totally unexpected.

Why the shape is so weird? It is a bit involved subject and we will try to cover it in another blog.

Relative sizes of the Halo orbit and other essential details are in the diagram below. 

 

Numerical values of different elements are listed in next figure:

 

Last 2 entries of subtended angles are of special interest to communications fraternity. 

It answers the common question that these people ask: How will the communication take place when there is a Sun radio noise is behind the satellite?

Sun disc is about half a degree across but the ADI orbit is at least  2 degrees away from Sun.

So when the Earth bound antenna is pointed to ADI ( which is in the orbit path ), the Solar noise does not enter the antenna because its beamwidth is less than 0.25 degrees and so the data carrier does not get corrupted with Solar noise.