PHY 101: Vector Integration

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What is Integration? Integration can be thought of as a continuous analogue of sum (\(\sum_{ }^{ }\)). We integrate or simply add infinitesimal small quantities together to form a continuous chain. Integration can be of 3 kinds rather I would call it 3 ways of integration. Linear, Area and Volume way. To show what each of them looks like here is a visual representation: $$\begin{aligned}& Linear \hspace{1mm}integration:\int_{ }^{ }f(x)dx\\ \\ &Area\hspace{1mm}or\hspace{1mm} surface\hspace{1mm} integration: \iint_S f(x,y)dxdy \\ \\ & Volume \hspace{1mm} integration: \iiint_V f(x,y,z)dxdydz \end{aligned}$$ You might have already noticed that the number of integration symbols (\(\int_{ }^{ }\)) increases with the increase in the number of variables. Hence, most books adopt the notation of calling these single, double and triple integrations. We at physics are creatures of simplicity and thus have kept it easy to remember. Let us talk about each in some detail! Single or Linear...

Chandrayaan 3: The Journey to the South of the Moon

Indian Space Research Organisation (ISRO), has taken up the challenge to conquer the South Pole of the Moon, with their Chandrayan-3 mission. This mission is being conducted after 4 years of the Chandrayan-2, which unfortunately crashed into the Lunar surface. The whole country awaits its successful landing at 6:04 pm (IST) on 23rd August 2023.

Understanding the significance of the South Pole

Since 1994 missions conducted by NASA, we determined the signs of water on the Lunar Surface, and with Chandrayan-1(ISRO) we confirmed these signs. Although we never actually traversed the south pole of the moon. Till now no country has landed on the south pole of our lunar satellite. It is believed there are pockets of frozen water(Ice) on the southern side, which is often not visible from our surface here on Earth. Thereby it becomes immensely important why this mission is a must-need success for the ISRO.

Signs of water on the southern side of lunar surface

Credits:https://www.nasa.gov 

Chandrayaan-3: Revisiting the Moon's Surface

Overview of the Chandrayaan-3 mission

Chandrayaan-3 is the third lunar mission by ISRO, building upon the success of Chandrayaan-1 and Chandrayaan-2(orbiter). The mission aims to demonstrate the safe and soft landing on the moon’s surface, roving of a rover on the lunar surface, and conducting in-situ scientific experiments. 

Differences from previous Chandrayaan missions

Chanadrayan-2 was aimed at studying the lunar surface, its mineral composition, and water ice presence in the polar regions. While Chandrayan-3 is aimed for a soft landing on the moon’s south pole, successful roving of the rover on the lunar surface and water ice presence on the lunar soil. Cahndrayan-3 has 3 parts, the propulsion module(PM) which will act as an orbiter, the landing module(LM)(VIKARAM), and the rover(PRAGYAN).

Why is Chandyana-3 better than Chandrayan-2?

ISRO has revised its launching of Chandrayan-3 by reviewing the failure of the landing module of Chandrayan-2. They have added a lot of safety measures for the successful landing of the lander module on the lunar soil. The measures taken by ISRO are:

1. Altimeters: Laser & RF based Altimeters

2. Velocimeters: Laser Doppler Velocimeter & Lander Horizontal Velocity Camera

3. Inertial Measurement: Laser Gyro based Inertial referencing and Accelerometer package

4. Propulsion System: 800N Throttleable Liquid Engines, 58N attitude thrusters & Throttleable Engine Control Electronics

5. Navigation, Guidance & Control (NGC): Powered Descent Trajectory design and associate software elements

6. Hazard Detection and Avoidance: Lander Hazard Detection & Avoidance Camera and Processing Algorithm

7. Landing Leg Mechanism.


(credits:https://www.isro.gov.in/Chandrayaan3_New.html )

The Lunar Landing Challenge

Landing on the Moon poses numerous challenges such as the absence of an atmosphere and the presence of uneven terrain. The lack of atmosphere on the moon is a challenge as they will need to eliminate the horizontal and vertical velocity with precision because of the vacuum in space and no air resistance. The uneven terrain also makes a difficult case, the lander has to find a creator probably for a safe landing as the tilting of the LM may lead to tripping of the module and crashing on the surface.

Ensuring a successful touchdown

To ensure a successful landing, Chandrayaan-3 has a multi-stage landing approach.

LM has been given a lot of extra fuel for emergency hovering, a reduced number of engines on the LM for low thrust, better software integration with sensors, better landing site selection, and the weight of the lander is also less,  legs of the LM are stronger and more durable.

Instruments and Payloads

https://www.isro.gov.in/Chandrayaan3_New.html, The link provided has the details about the instruments and payload in use for the Chandrayan-3 mission, this page is owned by ISRO.

Summary

Chandrayan-3’s journey to the moon is definitely an inspiring moment for not just the world but future generations to come. The success of this mission will definitely be a  great feat achieved by ISRO as the budget for this mission is about 615 crore rupees which is less than the previous moon mission Chandrayan-2. The launch of this mission took place on July 14, 2023, from Sathish Dhawan Space Center at Sri Harikota using the LVM3-M4 rocket. This mission will if successful, make India the first country in the world to land on the south pole of the Moon. Here are some pic of the PM, LM, and Rover:

Propulsion Module(PM)

Credits: https://www.isro.gov.in

Landing module(LM)(Vikaram)

credits:https://www.isro.gov.in


Rover(Pragyan)

credits:https://www.isro.gov.in

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