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[helen_mac]

can anyone tell me how the 'slingshot effect' works, our teacher skipped over it and i can't quite grasp the concept. thnx

 

[Gowr]

Okay...

Now, the slingshot effect refers to the speed increase due to an elastic collision between a planet and a ship. If the ship changes direction completely, then it gains the largest speed increase. How?

Well, we know that there is an elastic collision, which as a result means that both energy and momentum are conserved.

Given -v1i = initial speed of ship
v1f = final speed of ship
v2i = initial speed of planet
v2f = final speed of planet
m1=mass of ship
m2=mass of planet
Note: All v are relative to the sun

We get -m1. v1i +m2. v2i = m1.v1f + m2.v2f (Conservation of momentum)

and 1/2 m1. (v1i)^2 + 1/2 m2. (v2i)^2 = 1/2 m1.(v1f)^2 + 1/2 m2.(v2f)^2

Now, considering it is beyond the scope of mere HSC physics... I shall leave out the algebra... but, the end result of this is

v1f (speed of ship) = (m1-m2)(-v1i)/(m1+m2) +2m2 (v2i)/(m1+m2)

Now, considering that the mass of the planet is orders of magnitude above that of the ship, whenever we see m1+m2 or m1-m2, this can be simplified to m2 or -m2 respectively

Doing this we get v1f (speed of ship) = v1i (speed of the ship initially) + 2v2i (speed of planet initially)

So... as you can clearly see, the slingshot effect is simply a process in which through an elastic collision with a planet a ship can increase its speed relative to the sun by twice the rotational speed of a planet.

 

[243_robbo]

our teacher said that we only have to know it qualitatively and the momentum calculations are not part of the syllabus, but screw that lets do it anyway

 

[s2indie]

err.. we just had to know what it was.

 

[Helstar87]

Ok guys, I'm gona try to expain the slingshot effect in plain english without the extra maths crap (sorry maths nerds)
anyway, ok so consider a space shuttle that moving towards jupiter. now you've all learnt that every object has its own gravitational field surrounding it right? ok so, when the shuttle enters jupiters field of gravity, it experiences a "pull" as its drawn closer to the planet. the shuttle will then be swung around the planet and propelled back the direction it came from at a speed of (the speed of the ship initially (vi) plus twice the speed of the planet initially (2pvi)). Now this extra momentum comes from the planet, so in theory the planet slows down marginally as the energies are converted. However, as the planet is so large, this loss in jupiters speed is MINIMAL and as the shuttle in small in mass (relative to jupiter) the speed is noticeable.
Sorry its a bit rusty as I havn't done this in over a year, but I hope that helped

 

[airie]

So what would the shuttle be propelled back, instead of being captured by the planet? Is it just the engines inside at work?

 

[zeropoint]

So what would the shuttle be propelled back, instead of being captured by the planet? Is it just the engines inside at work?

It's not actually the engines that cause it to propel back. As Helstar said, the gravitational influence of the planet rotates the velocity vector of the spacecraft relative to the planet into a direction which is aligned with the planetery motion. Since energy is conserved, the speed of the spacecraft relative to the planet is unaffected, only its direction changes.

For the maths nerds, denote the velocity of A relative to B by v_AB. Then using S for spacecraft and P for planet we have (prior to the collision)

v_SP,i = v_S,i - v_P

and after the collision:

v_SP,f = v_S,f - v_P

since the velocity of the planet is essentially unchanged.

Now

|v_SP,i| = |v_SP,f|
|v_S,i - v_P| = |v_S,f - v_P|
|v_S,i| + |v_P| = |v_S,f| - |v_P|
So
|v_S,f| = |v_S,i| + 2|v_P|

as Gowr pointed out before.

James

 

[airie]

Thanks

The gravitational influence of the planet rotates the velocity vector of the spacecraft relative to the planet into a direction which is aligned with the planetery motion. Since energy is conserved, the speed of the spacecraft relative to the planet is unaffected, only its direction changes.

This slingshot effect sounds like it's at work too when, say, a small asteroid, is being 'kicked out' by a planet. How is this (and with the shuttle too) different in the case where the asteroid is being captured instead? Does it have anything to do with the initial speed of the asteroid?

 

[zeropoint]

Thanks

No problem

This slingshot effect sounds like it's at work too when, say, a small asteroid, is being 'kicked out' by a planet. How is this (and with the shuttle too) different in the case where the asteroid is being captured instead? Does it have anything to do with the initial speed of the asteroid?

Interesting question. Well, from my (limited) understanding of orbital mechanics, the condition for the two bodies to execute a stable orbit is that their total energy is less than zero. In practise you would calculate this as

1/2 m_1 v_1^2 + 1/2 m_2 v_2^2 - G m_1 m_2 / r^2

where v_1 and v_2 are the orbital speeds of the objects relative to some stationary coordinate system (such as the sun). If the speeds of the planet and spacecraft are low enough to make that number less than zero, then the spacecraft will enter a stable orbit about the planet, rather than being slingshotted.

I'm trying to imagine how an asteroid could get `kicked out' of a planetary orbit but I'm just not seeing it. Unless I'm mistaken, if the initial energy of the planet-asteroid system is less than zero, then this energy shouldn't change over time, so the asteroid should never escape, unless of course some external source of energy is introduced, in which case the asteroid will escape if it reaches escape velocity (total energy goes greater than or equal to zero).

James

 

[Raginsheep]

Im pretty sure its to do with orbital shapes.

 

[zeropoint]

Im pretty sure its to do with orbital shapes.

What do you mean?

 

[airie]

Interesting question. Well, from my (limited) understanding of orbital mechanics, the condition for the two bodies to execute a stable orbit is that their total energy is less than zero. In practise you would calculate this as

1/2 m_1 v_1^2 + 1/2 m_2 v_2^2 - G m_1 m_2 / r^2

where v_1 and v_2 are the orbital speeds of the objects relative to some stationary coordinate system (such as the sun). If the speeds of the planet and spacecraft are low enough to make that number less than zero, then the spacecraft will enter a stable orbit about the planet, rather than being slingshotted.

So you're saying that if the sum of the kinetic energy of both the planet and the spacecraft is less than the attraction between them, the spacecraft will be captured? Why would the kinetic energy of the planet be involved as well, instead of just that of the spacecraft? I just don't quite understand why the kinetic energy of the planet will have a role in determining if the spacecraft is captured or not. Am I allowed to picture it as, (excuse the inexact diction) if the kinetic energy of the planet is too big, regardless of how small that of the spacecraft is, it will still not be captured since the planet will just "run away", not "bringing the spacecraft with it" as its kinetic energy overcomes the attraction between them?

I'm trying to imagine how an asteroid could get `kicked out' of a planetary orbit but I'm just not seeing it. Unless I'm mistaken, if the initial energy of the planet-asteroid system is less than zero, then this energy shouldn't change over time, so the asteroid should never escape, unless of course some external source of energy is introduced, in which case the asteroid will escape if it reaches escape velocity (total energy goes greater than or equal to zero).

James

I meant to take an example of a moon of one of the planets in the solar system or something, but can't exactly remember which now Anyhow, would it help setting up the picture, if the scenario is this: a binary pair comes near the planet, one of them is captured by the planet while the other is sent out of the universe? Why aren't they both captured, or both experience the slingshot effect?

 

[fuckskooloff]

and where is the beer