Theme  Save the satellite 
Relevant Grades  Class 1112 (CBSE) 
Key Learning Objectives 

Session Duration  1 hour (Approximately) 
The Mission:
Students will be able to explain the concept of thrust of rockets and gravitational binding energy. The students are expected to create a game in which they have to control the thrust of an artificial satellite to avoid collision with asteroids and other satellite
 Concepts to Understand
2.1 Thrust
Thrust is a force that acts as a push to make an object move away from the other object. According to Newton’s third law of motion, every action has equal and opposite reaction.
For example, an aircraft engine acts on air and pushes it back. This causes the air to push the aircraft forward. Thus, air reacts on the aircraft to move forward. This reaction force is called as thrust.
2.2 Thrust in a rocket
Thrust produced by rocket make them propel forward. The gases formed by burning fuel are ejected at a very high speed. There is a push acting on these gases. Once these gases come out of the rocket, they apply reaction force on the rocket in the direction opposite to that of exhaust. As a result, rocket moves up, away from the earth.
As no external forces are involved in this, hence the linear momentum of the rocket is said to be conserved.
Let’s derive a rocket equation. Let’s say at time t, mass of the rocket with the fuel is m, and its initial velocity is v. At time t +
ΔΔ
t fuel burnt by rocket is
ΔΔ
m, which is converted into exhaust gases. The relative velocity of these exhaust gases is u. As a result of the exhaust, rocket gains velocity
ΔΔ
 Thus, the final velocity becomes v +
ΔΔ
 v.
Due to loss of fuel, the final mass of rocket at time t +
ΔΔ
t is m –
ΔΔ
m
The velocity of exhaust gases will be v – u.
According to the law of conservation of linear momentum, we can write
mv=(m−Δm)(v+Δv)+Δm (v−u)mv=m−Δmv+Δv+Δm v−u
On solving the above equation, we get
mv=mv+mΔv−Δmv−ΔmΔv+Δmv−Δmumv=mv+mΔv−Δmv−ΔmΔv+Δmv−Δmu
Solving the equation and ignoring the term
ΔmΔvΔmΔv
as it is negligible, we get,
mΔv=Δmu …(1)mΔv=Δmu …(1)
Next, dividing both the side by
ΔΔ
t we get
m{Δv}{Δt}=u{Δm}{Δt} …(2)mΔvΔt=uΔmΔt …(2)
At time t, mass of the rocket is m, and at time t +
ΔΔ
t the mass of the rocket is m –
ΔΔ
m
Taking the difference in the initial and the final mass we get,
m(t+Δt)−m(t)= m−Δm−m= −Δmmt+Δt−mt= m−Δm−m= −Δm
Differentiating the equation 1 and considering the mass difference we get
mdvdt= −udmdtmdvdt= −udmdt
T= ma= −udmdt …(3)T= ma= −udmdt …(3)
Thus, the thrust produced by the rocket is given by the equation (3).
On integrating the equation
mdv= −u dmmdv= −u dm
for the limits of velocity vi to vf and the limits of mass mi to mf, we get
m∫vfvidv= −u ∫mfmidmm∫vivfdv= −u ∫mimfdm
On solving the above equation, we get the equation of velocity of rocket as
[Math Processing Error]
For any rocket to take off the ratio of the thrust produced by it to its total weight should be always greater than 1.
The thrust to weight ratio is given as:
TW=mamg=agTW=mamg=ag
The more the acceleration produced by the rocket, the faster it can escape the gravitational pull of the earth.
2.3 Orbital velocity and gravitational binding energy
Once rocket lifts any satellite to a certain height, called its parking orbit point, then the satellite needs to start revolving into this orbit with some velocity v. if the satellite fails to do so, then it will crash back to the earth.
The work done in taking satellite to reach to the height dr, is dW = F x dr. here F is the gravitational force.
On integrating the equation for the limits of the height dr from h1 to h2 we get
∫dW= ∫h2h1GMEmr2 dr∫dW= ∫h1h2GMEmr2 dr
W=GMEm×(1h1−1h2)W=GMEm×1h1−1h2
Substituting h1 = R, and h2 = h for h > R, we can substitute for the WR as gravitational potential at the earth i.e. W0 in the above equation we get
W=GMEmh+W0W=GMEmh+W0
This equation gives the potential energy stored in the rocket at the height h. This energy is then converted into kinetic energy by a small push by the thruster in the satellite itself.
T hus the satellite captures the orbit and starts rotating around the earth.
The centripetal force acting on the satellite is
Fc=mv2oRe+hFc=mvo2Re+h
And the gravitational force acting on the satellite is
FG=GMem(Re+h)2FG=GMem(Re+h)2
As Fc = Fg hence we can write
mv2oRe+h=GMem(Re+h)2mvo2Re+h=GMem(Re+h)2
v2o=GMeRe+hvo2=GMeRe+h
Thus, taking square root on both the side we get
vo=GMeRe+h−−−−−−√= gRe−−−√vo=GMeRe+h= gRe
This equation gives the orbital velocity of the satellite with which it should move in the orbit at the height h above the Earth’s surface.
And the binding energy of the satellite becomes
E=mv2o2+W0=GMemh+W0E=mvo22+W0=GMemh+W0
2.4 Escape velocity
If a satellite has velocity
v=2gRe−−−−√= 2GMe/(Re+h) −−−−−−−−−−−−−√v=2gRe= 2GMe/(Re+h)
then the satellite does not stays in orbit and it flies away from the earth.
GAME DESIGN
Problem statement:
A vital communication satellite is orbiting around earth at a height of 800 km. An asteroid of length 500 m is approaching the satellite and will potentially crash on to it. In order to avoid the collision, a thrust has to be given to the satellite so that it climbs to a higher orbit that is at height 802 km. Up to a height of 805 km, the communication will not be affected. If the height goes any higher than 805 km, then the satellite may lose its communication functionality and also collide with debris.
Game Design Overview:
You are a flight controller working in the top most space agency in India. Your job is to ensure that satellites don’t ending up colliding with debris, asteroids or loose its path. In this case, you encounter a situation where a satellite is about to be hit by an asteroid, the asteroid is approaching your satellite very rapidly. If no action is taken, you will lose the satellite and the game will be over. In order to avoid the collision, you need to apply a calculated value of thrust by taking into consideration of the different parameters.
How to Design the Game:
Step 1:
Create a sprite of the satellite and set it in orbit around the Earth. The distance of the satellite from the earth’s surface is 800 km.
Step 2:
After sometime, suddenly a warning appears on your screen stating that an asteroid is heading towards the satellite
Step 3:
Use the thrusters, quantify the thrust applied by a specific amount such that the satellite climbs the orbit 2 km. The satellite can be controlled by applying thrusters in all directions.
Hint: The thrust should be applied such that the orbit climbs by 2km, if any further, then the satellite orbit will permanently change.
Step 4:
If the asteroid hits the satellite, then the game will be over.
Step 5: (Optional)
Level 2 can be built in the game with multiple asteroids appearing to hit the satellite.
Assessments:
Learning Objective Based Evaluation (02)  Q1  Q2  Q3  Q4  



 
Higher Order Thinking Skills  Problem Solving  Critical Thinking  Innovation  Creativity  
Q5  Q6  Q7  Q8  Q9  Q10  






Learning Objective Based Evaluation Total Score  /4 
Higher Order Thinking Skills Total Score  /8 
Total Score  /12 
Learning Objective Based Evaluation
1 point Questions:
Q1. The _________ acts as a consequence of combustion of gases/fuel in the rocket causing the rocket to propel forward
 action force
 reaction force
 retarding force
 electrostatic force
Q2. The thrust to weight ration is given as ________
Q3. Why it is important to have thrusters in artificial communication satellites?
 It is important for making the journey through the entire solar system and back
 To come back safely on earth
 To do orbital manoeuvring, corrections and keeping it in the same orbit as desired
 To reach moon
2 point Question:
Q4. Why is there a need for doing all the calculations correctly before launching a satellite?
 A lot of money is invested in space missions, it is important to plan it accurately and effectively
 To ensure the success of the space mission
 To launch the satellite successfully in the desired orbit
 All of the above
Evaluation of HOTS (Higher Order Thinking Skills)
Identification of the Problem Statement:
Q5. What is the objective of the game that you have designed? (1 point)
_____________________________________________________________
Q6. Does the game designed solve the problem? Justify your answer. (1 point)
_____________________________________________________________
Solution of the Problem Statement:
Q7. How does the game designed address the problem? (1 point)
_____________________________________________________________
Q8. Can the solution be implemented in real life? Justify your answer (1 point)
_____________________________________________________________
Innovation in the Problem Statement:
Q9. What are the innovative aspects of the solution for which the game is designed? (2 points)
_____________________________________________________________
Creativity in the Game Design:
Q10. Describe and explain the unique design elements used in the game. (2 points)
_____________________________________________________________
Disclaimer: This document is meant to be used for educational purposes only. The content here has been curated from various online sources. We do not intend to infringe on any copyrights. Please note that there are third party links in this module and Atal Innovation Mission or NITI Aayog does not endorse any person(s) or organizations mentioned on or related to these links.