The Wild Blue Yonder Page #2

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of the solar system.

It could radio back images

from the planets it encountered.

They named the probe Galileo.

They waited weeks.

They waited months.

And then these images came back.

Images that proved that there was no

hospitable place anywhere nearby.

It was clear now that there

was nothing nearby.

On the ground they knew they

needed a bolder plan

a trip beyond our

immediate horizonts.

For the mathematicians it was

only a question of a different trajectory.

The potential energy doesn't

change, that is the zero.

This velocity thing says that this

derivative comes out to be vdelta v.

It just required the gravity assist from Venus

and a fly-by of Jupiter.

It looked doable.

If we look at our

standard v equation

the key is going to be getting the right

v infinity of Venus.

We are still going to need enough

performance from the spacecraft

so that we can go below the orbit of Venus.

And also that the v infinity of Venus is high enough

that when we have to come up with the velocity needed

to get us on up to Jupiter that that will work.

I guess we could use this

to look at leaving the solar system.

For example this is the Sun.

The Earth is going around it.

Instead of thinking of this being a fixed

plane with the Sun in the center

and the Earth going around.

Let's just draw an axis

and rotate the plane with the Earth

so now the Earth looks like it is fixed.

Now we are working in a rotating system.

In this rotating system

if we have a little spacecraft,

an intender or whatever.

Moving around, it has got

some velocity in the rotating system.

And it's got potentional energy with respect to Earth and

potentional energy with respect to the Sun.

The Jacobi constant is equal to

one half the rotating velocity squared,

and I believe by convention it's all minused

so we get a negative sign on a kinetic energy,

and we have the gravitational constant of

the Sun divided by our distance from the Sun

and the gravitational constant of

the Earth divided by our distance from the Earth.

Whenever we come by the Earth, no matter which

direction we come in or which direction we fly by

we are going to end up with exactly the same velocity.

And the key then is to use other planets...

That's the wrong symbol.

That would be Mars

and it's in wrong place so we will

use Venus.... use other planets to

change what the Jacobi

constant is to a new value.

It's playing games with the Jacobi constant and

that's where the tour starts to get interesting.

On board, however, the shifted trajectory was

accepted as just an extension of their flight-plan.

The life carried on.

Day in, day out. Draggery set in.

As you get further and further away

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