INDIA'S MARS MISSION: HOW ORBITAL MECHANICS WORKS? (By Sanjeevi Ramamoorthy)
India has become the first nation in the world to have successfully achieved the Mars Mission in its Ist attempt itself. Only 3 Countries (USA, Russia & India) & 1 Continent (Eurpoean Space Agency) out of 200 countries in the world have so far successfully sent the orbiter to the mars. There have been 52 attempts by the various nations in last 60 years to send the orbiter to mars. But only 22 missions have become successful. ( Approx. 40 % Success rate).
How Inter Planetary Spaceflight Works?
There are two ways to send the Spacecrafts to the mars. Shortest Way ( Less time Consuming Method) is called as crow flight method / brutal force method in which spacecraft is sent from the earth orbit to mars against the sun's gravity through the continuous force generated by the burning of rocket fuel as explained in the below image.
(Illustration of Crow Flight Method)
However, it is not practically viable due to the requirement of Huge Fuel ( Since we lack the knowledge of any other method to accelerate Spacecraft in space except Newton's Third Law and Gravitational Sling Shot ( which is not effective between earth and mars)).
How Hohhman Transfer Orbit works?
Most economical method of sending spacecraft to mars which all nations currently follow is called as Hohhman Transfer Orbit Method.This is the most economical way of sending space craft since it consumes very less fuel but time consuming ( around 9 months to reach Mars).
According to this method, spacecraft will be transferred from earth's orbit to the Heliocentric orbit ( orbit around sun) first which is marked in green color in the below diagram.
Why it consumes Less Fuel?
It is because of Heliocentric Orbit & Newton's First Law. Burning of Fuel is only needed to transfer the spacecraft ( to attain the escape velocity to get out from the influence of earth's gravity) from the earth's orbit to Heliocentric orbit. Once it is done, it will simply start orbiting around the sun in Heliocentric Orbit like earth and all other planets normally do. Newton's First Law allows this space craft to be in constant motion without consuming further fuel.
Hohmaan Transfer orbit is nothing but highly Elliptical Orbit around sun which connect both earth's orbit and destination planet's orbit ( in this case Mars). The above diagram clearly shows the Heliocentric orbit in green color connecting both earth's and mars orbit.
Most critical aspect of this method is that mars & space craft should exactly reach the apogee ( furthest point of the Heliocentric orbit marked as red dot) in the same time to make the "Mars Orbit Transition (MOI)" possible. It happens only one time in approx. every 2 years. ( 2014, 2016 & 2018).
INDIA'S LIMITATION & HOW IT ENCOUNTERED:
Even though, we have successfully sent the orbiter to the mars, we lack the the powerful rockets like NASA's Atlas V (which can lift upto 18 MT) to carry the Heavy Spacecraft to space and to achieve the escape velocity ( 11. 2Km /s) to move out of earth's gravity pull.
Our PSLV can lift upto 1.3 MT only and can place the spacecraft only in Low Earth Orbit ( < 500 Km from the earth surface). It lacks the capability to directly inject the mangalyan in Mars Transfer Orbit (HeliocentricOrbit) . Only solution for this problem is to use the Method Called Orbital Maneuvers.
Earth Orbit Maneuvers:
According to the Kepler's 3rd Law, orbital speed of the spacecraft will increase due to the gravity when it reaches perigee ( closest point in the elliptical orbit) and decelerate when it moves towards apogee ( furthest point in the elliptical orbit) .
So If we fire the Liquid Apogee Motor (LAM) exactly when it reaches perigee ( as illustrated in below diagram, we can increase the distance of apogee ( which means that velocity of spacecraft will get increased as per Kepler IIIrd Law when it reaches perigee again). This method is called Earth Orbit Manuevers. See the below video to know exactly how it works.
( Video Illustration of Earth Orbit Maneuvers Method?)
After 4- 5 earth Maneuvers ( around 1 Lakhs Km apogee distance), mangalyan had attained velocity ( 11.2 Km/s) sufficient enough to escape from earth's gravity and to get transferred into Heliocentric Orbit.. This process is called Trans Mars Injection.
( Mangalyan's Earth Orbit Maneuver to attain the escape velocity)
Once spacecraft reaches Heliocentric Orbit, newtons first law will help it to reach mars orbit with out consuming fuel.
MARS ORBIT INSERTION:
Once Mars & Space craft reaches the apogee of Heliocentric, next challenge is deceleration.
Challenge in this phase is to decelerate the Spacecraft to a level where it wont escape the gravity of mars. But risk is that deceleration beyond the certain limit will lead the spacecraft to crash in mars surface. Challenges are to get the spacecraft into the capture orbit of Mars ( approx within 1 Lakh KM) and to decelerate it to < 2Km/ s velocity.
( Isro's simulation video explaining how Mars Orbit Transition Works)
Another efficient method to accelerate and decelerate the spacecraft without consuming fuel is Gravitional Sling Shot in which orbital energy of the planets is being converted to accelerate the body and vice versa. But it is not effective between earth and mars. NASA's Interplanetary missions such as Volyager1, Voyager II, New Horizon have sucessfully used this method to travel to the end of our solar system.
1.HOW GRAVITATIONAL SLING SHOT WORKS? CAN WE USE THIS METHOD FOR INTER GALACTIC TRAVEL?
2. IS FASTER THAN LIGHT TRAVEL POSSIBLE?
3. WHETHER "WARM HOLE" IS THE EASIEST WAY TO REACH OTHER GALAXIES?
4. CAN "SPACE - TIME" CAN BE WRAPPED ACCORDING THE EINESTIN'S GENERAL THEORY OF RELATIVITY?
( Let's discuss in the Part 2 of this article)
India has become the first nation in the world to have successfully achieved the Mars Mission in its Ist attempt itself. Only 3 Countries (USA, Russia & India) & 1 Continent (Eurpoean Space Agency) out of 200 countries in the world have so far successfully sent the orbiter to the mars. There have been 52 attempts by the various nations in last 60 years to send the orbiter to mars. But only 22 missions have become successful. ( Approx. 40 % Success rate).
How Inter Planetary Spaceflight Works?
There are two ways to send the Spacecrafts to the mars. Shortest Way ( Less time Consuming Method) is called as crow flight method / brutal force method in which spacecraft is sent from the earth orbit to mars against the sun's gravity through the continuous force generated by the burning of rocket fuel as explained in the below image.
(Illustration of Crow Flight Method)
However, it is not practically viable due to the requirement of Huge Fuel ( Since we lack the knowledge of any other method to accelerate Spacecraft in space except Newton's Third Law and Gravitational Sling Shot ( which is not effective between earth and mars)).
How Hohhman Transfer Orbit works?
Most economical method of sending spacecraft to mars which all nations currently follow is called as Hohhman Transfer Orbit Method.This is the most economical way of sending space craft since it consumes very less fuel but time consuming ( around 9 months to reach Mars).
According to this method, spacecraft will be transferred from earth's orbit to the Heliocentric orbit ( orbit around sun) first which is marked in green color in the below diagram.
Why it consumes Less Fuel?
It is because of Heliocentric Orbit & Newton's First Law. Burning of Fuel is only needed to transfer the spacecraft ( to attain the escape velocity to get out from the influence of earth's gravity) from the earth's orbit to Heliocentric orbit. Once it is done, it will simply start orbiting around the sun in Heliocentric Orbit like earth and all other planets normally do. Newton's First Law allows this space craft to be in constant motion without consuming further fuel.
Hohmaan Transfer orbit is nothing but highly Elliptical Orbit around sun which connect both earth's orbit and destination planet's orbit ( in this case Mars). The above diagram clearly shows the Heliocentric orbit in green color connecting both earth's and mars orbit.
Most critical aspect of this method is that mars & space craft should exactly reach the apogee ( furthest point of the Heliocentric orbit marked as red dot) in the same time to make the "Mars Orbit Transition (MOI)" possible. It happens only one time in approx. every 2 years. ( 2014, 2016 & 2018).
INDIA'S LIMITATION & HOW IT ENCOUNTERED:
Even though, we have successfully sent the orbiter to the mars, we lack the the powerful rockets like NASA's Atlas V (which can lift upto 18 MT) to carry the Heavy Spacecraft to space and to achieve the escape velocity ( 11. 2Km /s) to move out of earth's gravity pull.
Our PSLV can lift upto 1.3 MT only and can place the spacecraft only in Low Earth Orbit ( < 500 Km from the earth surface). It lacks the capability to directly inject the mangalyan in Mars Transfer Orbit (HeliocentricOrbit) . Only solution for this problem is to use the Method Called Orbital Maneuvers.
Earth Orbit Maneuvers:
According to the Kepler's 3rd Law, orbital speed of the spacecraft will increase due to the gravity when it reaches perigee ( closest point in the elliptical orbit) and decelerate when it moves towards apogee ( furthest point in the elliptical orbit) .
So If we fire the Liquid Apogee Motor (LAM) exactly when it reaches perigee ( as illustrated in below diagram, we can increase the distance of apogee ( which means that velocity of spacecraft will get increased as per Kepler IIIrd Law when it reaches perigee again). This method is called Earth Orbit Manuevers. See the below video to know exactly how it works.
( Video Illustration of Earth Orbit Maneuvers Method?)
After 4- 5 earth Maneuvers ( around 1 Lakhs Km apogee distance), mangalyan had attained velocity ( 11.2 Km/s) sufficient enough to escape from earth's gravity and to get transferred into Heliocentric Orbit.. This process is called Trans Mars Injection.
( Mangalyan's Earth Orbit Maneuver to attain the escape velocity)
Once spacecraft reaches Heliocentric Orbit, newtons first law will help it to reach mars orbit with out consuming fuel.
MARS ORBIT INSERTION:
Once Mars & Space craft reaches the apogee of Heliocentric, next challenge is deceleration.
Challenge in this phase is to decelerate the Spacecraft to a level where it wont escape the gravity of mars. But risk is that deceleration beyond the certain limit will lead the spacecraft to crash in mars surface. Challenges are to get the spacecraft into the capture orbit of Mars ( approx within 1 Lakh KM) and to decelerate it to < 2Km/ s velocity.
( Isro's simulation video explaining how Mars Orbit Transition Works)
Another efficient method to accelerate and decelerate the spacecraft without consuming fuel is Gravitional Sling Shot in which orbital energy of the planets is being converted to accelerate the body and vice versa. But it is not effective between earth and mars. NASA's Interplanetary missions such as Volyager1, Voyager II, New Horizon have sucessfully used this method to travel to the end of our solar system.
1.HOW GRAVITATIONAL SLING SHOT WORKS? CAN WE USE THIS METHOD FOR INTER GALACTIC TRAVEL?
2. IS FASTER THAN LIGHT TRAVEL POSSIBLE?
3. WHETHER "WARM HOLE" IS THE EASIEST WAY TO REACH OTHER GALAXIES?
4. CAN "SPACE - TIME" CAN BE WRAPPED ACCORDING THE EINESTIN'S GENERAL THEORY OF RELATIVITY?
( Let's discuss in the Part 2 of this article)
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