But the fact I'd like to notice is that there's this exchange of energy, and it brings light for me on the question of how you can get a projectile to escape the solar system from launching it from Earth.  Like, how much energy would it need?

Now, you can calculate the sun's gravitational field into the question and realize that you've got to have enough energy to escape the sun's pull. But if you thought that you needed to put that much energy into the rocket, in terms of fuel in the rocket, that would be wrong.

Because you need a lot less fuel than that. This is something they took advantage of in the Galileo mission. They called it a slingshot effect or gravitational assist. And the way they described it, as I read it in the newspapers—and maybe I read it

wrong, and I'd have to go back and look at how they phrased the articles—but I believe they phrased it that they were using the powerful gravitational field of Jupiter to give the projectile a boost, as a slingshot effect. That it would go near

Jupiter and be boosted forward on its path. And I used to wonder, well, how can a gravitational field do that? Because if Jupiter is accelerating the projectile towards it, then it's picking up speed. But once you pass Jupiter, the pull is the other way.

So then you're losing speed. And certainly, by conservation of energy, you should think that anything that the gravitational field puts in, it has to take back. What you gain as you're approaching, you have to give back as you're receding. And this is true.

It's true; there's no energy to begin with from the gravitational field. The source of energy is the kinetic energy of motion which Jupiter possesses by virtue of the fact that it's moving. That's the energy that the whiplash effect puts into the spaceship.

And gravity acts only as a medium for the exchange to take place. As a matter of fact, you can see much more easily how the effect occurs if we neglect gravity altogether and imagine that the spaceship is a little steel ball bearing and that Jupiter

is a solid steel ball, and we can say it's a hollow ball so that it's very light, so it has no mass and let's say it has no gravitational field. You could imagine it being hollow but still having a hard shell, so the satellite just bounces off it

like a ping-pong ball. And if you think of it that way, it's not hard to believe that if you give the satellite just enough energy to reach the outer reaches of the solar system, as far as the orbit of Jupiter, so that it's just dead in the water when

it reaches the point of Jupiter, but at the same point Jupiter is swinging around like a ping-pong mallet, strikes it; it could knock it right out of the solar system. And that's the mechanism whereby energy is given to the satellite.

It's an interesting thing that it works just as well if they don't actually collide physically, but when the interaction is through gravity, which acts at a distance, that's really irrelevant to the exchange of energies which takes place. How can we say it? Yeah, from the point of

A view of someone watching the interaction from Earth. Just consider the fact that the sun is over here, the Earth is over here, Jupiter is far away. The satellite approaches Jupiter—and I haven't drawn that very well.

I haven't drawn that well. No, I haven't drawn that well. I might as well draw it well. If it were a ping-pong ball, you might want to shoot it up so that it goes—ping!—okay? Because this is moving forward, and

that would be how you'd want to—you'd want to bounce it off if you're doing it as a ping-pong ball. Well, drawn to scale, Jupiter is tiny; it's so tiny you can't even see it. And if we blow up this picture, if we expand

it to where we can look at it, what's happening on a large scale, then if the interaction was of this kind, where it was strictly through a pull of gravity rather than through bouncing off and striking it... Look at the boundaries of my square: I've

got something coming in here and going out here at this angle, and this is going out at a different angle with a different speed. Now let's pan over to that little square over here on the board, and you'll see I'm—I'm coming in and

going out the same way. Like, the net inputs and outputs of the process are the same. And here I was picturing it as a ping-pong ball, but it could have just as well happened as a gravitational—what they call—a slingshot effect.

The reason it's nice to do it as a ping-pong ball is that, even in grade 11, we learned enough physics to be able to analyze these ping-pong ball collisions. If we wanted to analyze this gravitational one, it would be complicated; we'd have to use

calculus and a lot of things like that because we'd be all worried about the slight changes in the curvature of the trajectory and everything. But we learned in grade 11 that when something interacts like a ping-pong ball, it's very simple to do the calculation.

As long as you satisfy two conditions: the total momentum of the system does not change during the interaction, and the total energy of the system remains constant. We can exchange energy between the two projectiles—the small one and the big one—but the total has to be the same.

Slingshot Effect

Martin Green

Energy exchange and escaping the solar system

Exchange of energy is key to launching a projectile out of the solar system.

Calculating the sun's gravitational field is crucial, but the required fuel is less than expected.

The Galileo mission used the slingshot effect or gravitational assist.

Jupiter's gravitational field boosts the projectile, but the speed is lost after passing Jupiter.

The energy comes from Jupiter's kinetic energy of motion, not the gravitational field itself.

The slingshot effect explained using a simplified model

A simplified model using a steel ball bearing (spaceship) and a hollow steel ball (Jupiter) is introduced.

The satellite bounces off Jupiter like a ping-pong ball.

If the satellite has enough energy to reach Jupiter's orbit, Jupiter's movement can knock it out of the solar system.

The physical collision isn't necessary; the energy exchange works through gravity.

Visual explanation of the energy exchange

A visual representation of the satellite approaching and leaving Jupiter is presented.

The analogy of a ping-pong ball is used to illustrate the trajectory.

Jupiter's size is emphasized to show the scale of the interaction.

The angles and speeds of the satellite before and after the interaction are compared.

The net inputs and outputs of the process are the same, whether it's a ping-pong ball collision or a gravitational interaction.

Physics principles involved in the energy exchange

Analyzing the ping-pong ball collision is simpler than analyzing the gravitational interaction.

The analysis requires satisfying two conditions: conservation of momentum and conservation of energy.

Energy can be exchanged between the satellite and Jupiter, but the total energy remains constant.