INTERPLANETARY TRAVEL

"The first day or so we all pointed to our countries . The third or fourth day ,we were pointing to other countries . By the fifth day , we were only aware of earth"-Sultan bin Salman Al-Saud

Curiousity about space is the essence of human existence. So , this blog post is about some of the tricks that we are using for interplanetary travel.

Well why do we need to use them though ?

Because they are more efficient . Planets, let alone galaxies are millions of kilometres away from us and exploring them requires efficiency in fuel and time . This is what is provided by these tricks.


Getting away from Earth ; The pale blue dot

Want to escape from solar system , make the total energy of trajectory = 0

What's total energy ? It's the sum of -

Kinetic Energy - energy due to motion +
Potential Energy - energy due to configuration
Putting total energy 0 we get escape speed from Earth = ( 2* G *M /R) ^ (0.5) where ,
G = Gravitational Constant -6.6× 10^ (-11) Nm^2 kg^2
M = Mass of Sun = 1.98 * 10^30 kg 
R = Distance of sun from Earth = 152.09 million km

Putting all these values we get escape speed from earth - 11.2 km /s 

Long story short, The spacecraft launched in any direction will reach the out of the Gravitational pull of earth when launched with the speed 11.2 km/s.


Getting to other planets :

Hohmann Transfer

Credit:Wikipedia

Hohmann ( a German scientist) showed that the lowest propellant path between any two orbits is an elliptical orbit which forms a tangent to the starting and destination orbits.
(Pic)

Insight - Spacecraft to Mars and Chandrayaan-Spacecraft to moon used this technique

Calculating launch speed to other planets

Suppose we launch from the Earth, at a distance R1 from the Sun, at a target planet a distance R2 from the Sun. 

Let r denote the ratio R2/R1; then r is just the orbital radius of the target planet expressed in astronomical units (AU).
v⊕ = orbital speed of the planet from where the spacecraft is to be launched 

To reach the outer planet, the spacecraft is required to have a speed relative to the Sun after escaping the Earth of:
v = (2r/r + 1)^ 1/2 * v⊕ 

For Jupiter we have this speed = 38.6 km /s
To get launch speed from Earth , subtract earth's orbital speed 29.8 km/s and add the escape speed.
Thus launch speed to Jupiter is 20 km/s 

Similarly, launch speed to a planet from any other planet can also be calculated.


Gravitational Slingshot -

 Using gravity of planet to reach to other planets

Now we have successfully sent our spacecraft to Jupiter , we will gravity of Jupiter to send it further and out of Solar System.
Wait ! If we send a spacecraft on a trajectory
around Jupiter , and we follow its orbit as it falls towards the planet and then comes
back out, we always find that it returns to the same place as we started it with exactly
the same speed. There is no gain! But we see Voyagers speeding up gaining speed from Jupiter. How's that possible?
Well answer lies in the 'frame of reference' .
We need to look at the change in speed through frame of reference of Sun:

It seems like breaking the conservation law, it seems like planet is taking energy out of the system out of nowhere . Well that's not actually the case .

The gain in speed of spacecraft is accompanied by slowing down of Jupiter a tiny bit , 

because Jupiter is very large , this slowing down isn't prominent enough . But yeah , with millions and trillions of similar slingshots , we can slow the planet to even such an extent that it will start dropping towards Sun's gravity .

This is pretty much what Voyagers have used to escape the boundaries of solar system.
Taking spacecraft approaching along different direction , we can slow down the spacecraft as well and make it fall close towards sun and speed up the planet.

Thus we see how we can use planets like controllers for our journey to the outer world.This realisation so freaking awesome in itself !
Not the gravity but time dependency of gravitational field due to motion of the planet has helped us in taking some advantage out of it . The conservation laws you see , are built on principle of invariance , invariance of gravitational fields , time .

The relation between conservation laws and invariance is built into the laws of physics at their deepest level. How can we mold them into our benefit is totally upon our understanding of phenomenon and curiosity in understanding the nature of Universe .

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