Chandrayaan-3: Let’s Unveil the Mission

 

Introductory discussion:

 

Recently, the mission called “Chandrayaan-3” has achieved remarkable success in the field of the lunar mission. But, most of the people are unaware about the question, “How was this mission solved and got great success by “ISRO(Indian Space Research Organisation)”? Moreover, this revolutionary mission of “ISRO” is one of the most cost effective Lunar missions in history. But, do we know why this mission is called cost effective? And what were the significant parts which form the total propulsion module and total designing system of the mission? The counters of these questions have a great relation with “Mechanical Engineering” knowledge, orbital dynamics and our well-known laws of physics. In this blog, the significant details of this revolutionary lunar mission will be unveiled.

    Picture 01: LVM3-M4 Rocket launching 

Formation of mechanical model : Chandrayaan-3 mission model is mainly formed of three main components (Propulsion module, Lander and Rover) which were carried by a rocket named LVM3-M4 from the earth's surface to “Low Earth Orbit (LEO)”. One of the significant parts of the rocket is “Large Solid Boosters(LSB) (Quantity-02)”. LSB provides huge thrust (F_Thurst= V_f . dm/dt) to the whole system and detach from the whole system after the fuel has burned. The propulsion module plays a significant role in case of orbital control of the spacecraft. This module provides necessary thrusts for the maneuver operations (Upto 100 km from the lunar surface). Now the other important part of the system called “Lander” named as “Vikram” is used for the safe and soft landing on the lunar surface. “Vikram”- the lander consists of a high resolution camera, different types of sensors, 4 landing legs, 4 landing thrusters (produces roughly 800 newton of each), 4 variable thrust engines and different types of scientific mountings. Inside the lander there's a rover named as “Pragyan” for performing lunar surface and soil research, atmospheric analysis and analysis of moons impact. 

Picture 02: Propulsion Module

Picture 2.1: Vikram Lander

Picture 2.2: The Rover (Pragyan)

Solving out the mission:

 

In brief, the overall “Chandrayaan-3” mission challenges  as follows:

 

 

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1. Approaching to the “Lower Earth Orbit (LEO)”

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2. Around earth Orbital control (Increasing altitude) by several maneuvers to gain escape velocity

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3. Trans-lunar injection

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4. Lunar orbit insertion

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5. Around moon orbital control (Decreasing altitude) by several maneuvers

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6. Lander deorbit

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7. Soft landing (The most difficult step)

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Solving out the challenges:

 

1. Approaching the LEO: The main challenge in this section is to overcome the gravitational pull of the earth. This challenge can be solved by using a propulsion rocket (LVM3-M4) (Picture-01)which contains two boosters that give huge thrust to lift up to the LEO.

 

2. Gaining escape velocity with minimum fuel cost: Direct escaping from earth's gravitational pull is not cost effective. Rather than direct path the “Planetary Slingshot” is more cost effective to escape from earth's gravitational pull because this method demands less fuel but relatively long time. The mechanism of planetary slingshot is to increase/decrease the altitude of an orbit by applying several maneuvers/burns/firing by using the propulsion module of the spacecraft [1]. To gain escape velocity the altitude should be high according to the following equation:

 

Vescape=(2GM/r)^1/2…………….(1)

The escape velocity of earth is 11.2 km/s. So, the goal is to achieve this velocity by applying maneuvers. After performing several earth bounded maneuvers (Prograde burn) (Ensured from the graph-01) the

Graph 01: The graph performed by matlab shows that the more altitude the less velocity required to escape earth's gravitational pull (By Matlab)

Spacecraft able to gain escape velocity with minimum consumption of fuel. Now, we’ll analyze the last orbit of the maneuvers whether the spacecraft gains escape velocity or not.

 

In case of any keplerian orbit the spacecrafts motion around the earth/any planet follows the following equation which is known as Burgas formula: [3]

 

Where,                                

 

    V= Velocity of the spacecraft along the orbit

G= Gravitational constant (6.67x10^-11 )

M= Mass of earth= 5.972х10²⁴ kg

 r= distance between the center of gravity of earth and the spacecraft at lowest distance (Periapsis)=  km

a= Length of the semi-major axis of the elliptical orbit (Last maneuvers about earth)= 63919.5 km (Reference Data [4] )

 

Plugging in the value’s in the equation (2).........

 

We get, The velocity of the the spacecraft at the periapsis point,

 

V_spacecraft= 10.671 km/s……….. (3)

 

Now, Pugging in the value of G,M and r in the equation (1) we get escape velocity (Now, a= ) required at periapsis point of the elliptic orbit,

 

V_escape= 10.792 km/s………..(4)

 

From equations (3) and (4) we can say that two values are too close even at the minimum distance point of the orbital. So applying commonsense we can say that this orbital is the orbital of escape because as the spacecraft moves the altitude will increase and velocity will also be higher than the periapsis point. So escape velocity has been gained by the spacecraft at the fifth maneuver.

Picture 03: Earth to moon landing process

 

 

3.Trans-lunar injection: This is one of the most important parts of the mission. When the spacecraft gains its escape velocity (Free from earth's gravitational pull) this propulsion module enters into the trans-lunar trajectory and reaches out the lunar orbit [2]. Now the spacecraft manages to match the speed of the moon

4. Lunar orbit insertion: The spacecraft manages to enter into the lunar orbit by performing maneuvers unlike the earth's maneuvers.

5. Decreasing the altitude: This time, the spacecraft manages to decrease the orbit altitude by performing “Retrograde Burn” that refers to the opposite thrust of the direction of motion of the spacecraft.

6. Lander de-orbiting from the propulsion module:  As the spacecraft reaches near the lunar surface, the propulsion module gets detached from the lander and the lander starts to deorbit by slowing down its speed along the orbital.

7. Soft Landing: This is the most difficult part of the mission when the “Chandrayaan-2” mission failed. There are four variable thrusters, four landing thrusters available for soft lunar landing and some sensors and a high resolution camera with the lander “Vikram”. They analyze the situations and perform perfect orientation of the lander to land on the lunar surface safely. Finally, the lander landed on the south pole of the moon for the 1st time in the history of mankind.

 

Why is this mission cost effective scientifically?:  The reason is, in this mission scientists use the gravity assist/planetary slingshot to lower the consumption of fuel which has already been discussed above. Except that, some other factors may affect the cost of this mission.

 

References:

 

1. Sawant, Pranav. “Chandrayaan 3 is the cheapest lunar mission: Comparison.” Techlusive, 23 August 2023, https://www.techlusive.in/news/isros-lunar-mission-is-cost-effective-1401188/. Accessed 21 September 2023.

 

2. “Chandrayaan-3 leaves Earth's influence after 17 days in orbit. Next stop: Moon.” WION, 1 August 2023, https://www.wionews.com/india-news/chandrayaan-3-leaves-earths-influence-after-18-days-in-orbit-next-stop-moon-621238. Accessed 21 September 2023.

 

3. Logsdon, Tom. Orbital Mechanics: Theory and Applications. Wiley, 1998. Accessed 21 September 2023.

 

4. @isro (25 July 2023). "The fifth orbit raising operation" (Tweet). Retrieved 25 July 2023 – via Twitter.

Appendix:

 

Matlab Simulation Code for graph-01:

 

%Start of code

 G=6.67e-11;

 M=5.972e24;

 r=linspace(1.6e5,1e6,1000);

 V=sqrt(2*G*M./r);

 plot(r,V);

 xlabel('Altitude in metre');

 ylabel('Escape Velocity in metre per second');

 title('Escape Velocity vs Altitude graph');

 grid on;

%End of code

 

 

 

[Picture-01,02,2.1 & 2.2 are collected by google search]