Nuclear waste and the sun

Factual Questions
1

I was recently reading a book called Everything You Know Is Wrong by Paul Kirchner. It is a sort of encyclopedia of common misconceptions.

For the most part, it seems to be pretty solid, but one part has me a little baffled. It says that the reason we don’t send our nuclear wastes into the sun is that it is difficult to send a rocket to the sun. It goes on to state that it is actually easier to send a rocket into deep space. Can some astronautics expert out there explain why it’s easier to send a rocket away from a large gravitational source than toward it?

2

Well, first off all, I think the main reason we don’t launch off our nuclear waste is because it would be extremely expensive, and a launch failure would be very messy.

But back to the Sun question. Well, a rocket leaving Earth would still have the momentum from the orbit of the Earth. If it barely broke escape velocity, it would be in orbit around the Sun along with the Earth. To launch the rocket into the Sun, the rocket would need to negate the momentum from the Earth’s orbit in addition to escaping the gravity of the Earth.

To launch a rocket into deep space, the rocket would need to overcome the escape velocity for the Earth, and then the escape velocity for the Sun as well. In this case, the momentum of the Earth orbit could be used to help escape the Sun.

So the easiest thing to do would be to allow the rocket to go up, and just stay in orbit around the Sun. Or course that could be dangerous if it wasn’t put in an orbit sufficiently far from the Earth and the Moon.

3

**Can some astronautics expert out there explain why it’s easier to send a rocket away from a large gravitational source than toward it? **

I’m no astronautics “expert” (I took one class about a decade ago), but what the hell - I’ll give it a shot.

The problem you’re probably having is with the popular conception of an orbit. You’re probably figuring that you’d point the rocket up at the sun, hit the “Go” button, and it’s all over - the rocket would shoot straight towards the sun and vanish in a puff at the end.

You have to take into account a couple of things. First, rockets only burn for a few minutes. What they do is get up to speed really fast & then coast along like sattelites in an orbit. You also need to take into account that the earth is going really fast around the sun - about 63,000 miles per hour. When you fire off your little rocket, it’s going pretty fast itself - but only about 17,000 mph. So, when your rocket craps out, you’re not making a beeline for the sun, but you’re in an elliptical orbit that has the Earth’s orbital radius as its apoapsis (the point furthest from the sun) and some other, non-inside-the-sun point as its periapsis (point closest to the sun).

In order to hit the sun, what you have to do is get yourself in an orbit that has Earth as its apoapsis and the surface of the sun as its peripasis. In order to do that, you need an orbital velocity of about 2.87 km/sec (relative to the sun). So, from a parking orbit (a circular Low-Earth orbit of about 200 miles), you wait until you get on the far side of the earth (so your orbital velocity is moving in the opposite direction of the earth’s revolution around the sun, you dig?). Then you fire your upper stage. But you’d better fire it hard, because you’re going to need another 25 km/sec (around 53k mph?) to overcome the earth’s orbital velocity & start dropping in toward the sun.

On the other hand, if, during this same parking orbit, you wait until you get on the daylight side of your orbit (where your orbital velocity around the earth is in the same direction as the earth’s around the sun, you dig?) and then fire your upper stage, you only need to add on 20 km/sec (about 42k mph) to reach an escape velocity that will allow you to leave the solar system and never come back.

So, after all that, the delta v (change in velocity) required for hitting the sun is about 5 km/sec higher than it is for escaping the sun, primarily because you’re starting from a platform that’s moving so goddamn fast in the first place.

They say I got the power, because I got the monkeys.
They are WRONG! I got the power because I am not afraid to let the monkeys loose.

4

wait until you get on the daylight side of your orbit

Durnit! On the daylight side you’re heading the wrong way - you’d have to do it on the night side. The main point is that if you want to escape, you get to add up all your speeds, but to hit the sun, you have to subtract.

5

This is a pretty pointless use of terminology, given that the only such orbit would be a straight line to the Sun. Unless of course you were suggesting an orbit around some body other than the Sun or the Earth. :wink:
If not, it would probably be a bit more effective just to say a straight line to the Sun.

6

Two Kentuckians (I live in Indiana) are building a rocket in their backyard. Guy stops to admire the workmanship, asks what they’re going to do with it. “Gonna fly to the sun!” sez Jim Bob. “What! You’ll burn up before you get within 50 million miles of the sun!” sez the passerby. “We got that all figured out,” sez Jim Bob, "we’re going at night!

7

That’s when I.R. Baboon went there too!

8

Thanks Darkfox, I love a good technical explanation. (Though I had to look up some of the terminology.)

I’m beginning to understand, but not completely. The misconceptions you mentioned toward the beginning of your post I already had a grasp of. What your saying (please correct me if I’m wrong) is that the additional velocity required to get out of the same orbit the earth is in is easier to achieve if you’re shooting for deep space.

Here’s where I’m still fuzzy. (I gotta replace that razor blade.) Escaping Earth’s gravitational pull is a necessity regardless of where you’re headed. Since we don’t need for the rocket to get to the sun immediately, is it really that much harder to get it going into a slow spiral that will put it in the sun at some indefinite point in the future?

9

For an orbit to spiral inward, there needs to be some sort of drag that constantly slows the orbit. If we shot off a rocket, and simply left it with less speed than the Earth has, it wouldn’t spiral. It would orbit. The orbit would just be a more eccentric ellipse. This adds an additional complication to the process of dropping the weapons into the Sun, beyond the additional energy required-- you actually need to aim! If the path of the rocket misses the Sun by far enough to avoid being destroyed, it will assume an elliptical orbit.

10

OK, Dude, but if that is true, shouldn’t Skylab still be in orbit around the Earth? What causes an orbit to decay, if it isn’t insufficient speed to maintain a constant state of “falling” around the point of gravitation?

11

I think Skylab may have been effected by a very, very, thin atmosphere. In addition, ferromagnetic objects (like spacecraft made with steel) moving through magnetic fields (like the magnetic field of the Earth) do experience a drag, but it is very weak. This drag happens because the large magnetic field induces a reversed, and therefore repulsive magnetic field in the craft.

12

Actually, left to drift, the rocket would eventually fall into the sun. This is for two reasons, one is that there is drag in space, in the form of intersteller dust, micrometeors, etc. In fact as I recall, the earth falls closer to the sun every year or so, though I am not certain how far, I seem to recall a foot a year. The other reason that the rocket would fall into the sun eventually…Because the sun would rise up to meet it when it starts to expand towards giant status. I didn’t say all this would happen quickly, just that it would happen. :slight_smile:

>>while contemplating the navel of the universe, I wondered, is it an innie or outie?<<

—The dragon observes

13

>In addition, ferromagnetic objects (like
>spacecraft made with steel) moving through
>magnetic fields (like the magnetic field of
>the Earth) do experience a drag, but it is
>very weak.

Does the sun have a magnetic field?

14

Say you’re in circular orbit around something, at a radius r from it (specifically, its center) and the gravitational field you’re experiencing is g.
Your orbital velocity is

v = sqrt(g*r).

At the same time, escape velocity is

v = sqrt(2gr).

(Proving this is left as an exercise to the reader. It’s a calculus problem.)

We are about 150 million km away from the sun. The Earth’s velocity is

v = 2pir/T = 30000 m/sec.

where r is the Earth’s distance from the sun (1.5*10^11 meters) and T is the time it takes the earth to do one complete orbit (31556900 seconds, or one year).

So you can solve for g (using either the 1st or 3rd equation above) and find that the sun’s gravitational field at this distance is

g = v^2/r = 4rpi^2/T^2 = 0.006 m/sec^2.

In comparison, the earth’s own field at the surface is 9.8 m/s^2.

 Now assume for the sake of argument that we have nuclear waste here on Earth. We have two ways to get rid of it:

A. Pitch the nuclear waste into the sun.
B. Hurl the nuclear waste out of the solar system.

For plan A, the velocity of the waste must be zero relative to the sun so that it can fall right in. (This is an oversimplification; to be specific, it’s the tangential velocity that must be zero.)
For plan B, the velocity must be sqrt(2gr)=42500 meters/sec relative to the sun.

A key factor in making the decision is the current speed of the waste, which is sitting on Earth. The waste is already moving at 30000 m/sec. (We’re going to neglect the escape velocity from the Earth itself, which is 10000 m/sec if you’re curious. And trying to take advantage of the day/night velocities will hardly net you anything. The Earth’s rotational velocity at the equator is only about 440 m/sec.)

For Plan A, we have to throw the waste 30000 m/sec in the direction opposite the Earth’s motion. For Plan B, we only have to throw it 42500-30000 = 12500 m/sec. So Plan B wins.

Complicating this is that the current velocity, 30000 m/sec, is tangential, and the direction we’re going to pitch is normal to the Earth’s orbit. So you need to use vector addition which is a bit harder to draw here with text. Still, 12500 is roughly correct, and I want to go to bed soon. A further complication comes from the fact that “escape velocity” calculations implicitly assume that the payloads are shot from cannons instantaneously and experience no acceleration afterwards. In the real world, we use rockets, which accelerate things gradually over time. You don’t need to achieve escape velocity if you still have enough rocket fuel left and can get far enough away. Plus, rocket fuel weighs quite a bit just by itself. You get the picture.

The best plan, really, is:
C. Put the waste on a truck headed to Nevada, which requires only 65 mph.

15

Let us pre-suppose that the course can be plotted. Let’s figure out the cost of shipping a significant amount of waste.
There’s payload weight, shielding, getting ANY states permission to do something that dangerous, etc. Anybody want to help me here?

“When the going gets weird, the weird turn pro.”
Hunter Thompson

16

Definitely. It has a very complicated magnetic field, given the effects of sunspots.

As you are probably alluding to, it is likely that the rocket would eventually fall into the Sun, even if it is in an orbit similar to that of the Earth. This isn’t very useful for the task at hand since that could take millions, if not billions of years.

17

::flashes back to school texts::

Sure, but escape velocity is fairly analogous to the kinetic energy required, and KE wouldn’t have that restriction. Escape velocity also looks a bit more meaningful to the average reader than would a value in joules. :slight_smile:

18

Undead Dude sez:
This is a pretty pointless use of terminology, given that the only such orbit [an orbit that has Earth as its apoapsis and the surface of the sun as its peripasis] would be a straight line to the Sun.

Not at all! Remember, we’re talking about an orbit around the gravitational center of the sun. Think of a marble with the mass of the sun. You could have an elliptical orbit with an apoapsis of 1.5x10^8 km (earth’s orbit) and a periapsis of 696000 km (the sun’s radius). You’d actually orbit around the sun & hit the surface on the back side. This technique (using an elliptical orbit between two circular ones) is called a Hohmann transfer & is the lowest-energy transfer that uses impulsive thrusting (like liquid rockets).

Undead Dude also sez:
*** I think Skylab may have been effected by a very, very, thin atmosphere.***

Exactly. Objects in Low Earth Orbits are still affected by the atmosphere, which doesn’t just abruptly stop somewhere. Normal orbits don’t degrade unless some outside force degrades them. The current International Space Station needs to be reboosted all the time or else it too will drop on Australia.

Lipochrome sez:
For plan A [dropping nuke waste into the sun], the velocity of the waste must be zero relative to the sun so that it can fall right in.

No. Doing this would work, but it’s a very high-energy solution. If you slowed down the waste enough, you could get it to take an elliptical path to the sun (can we all agree that relying on interplanetary drag is cheating?).

He also sez:
And trying to take advantage of the day/night velocities will hardly net you anything. The Earth’s rotational velocity at the equator is only about 440 m/sec.)

Yeah, but remember - I was using that in the context of a low-earth parking orbit, where your velocity is 7600 m/sec, which helps a little more. I did mix up the day/night sides, though.

They say I got the power, because I got the monkeys.
They are WRONG! I got the power because I am not afraid to let the monkeys loose.

19

I thought some poorly-drawn visual aids might help out here.

First, here’s the orbit I’m talking about that will drop the trash into the sun:

http://members.xoom.com/ffungo/trashorbit.gif

It’s an elliptical orbit that’s a lower-energy orbit than earth’s, so the trashball has to go slower than earth at the same point. Notice that, since the orbit goes around the center of the sun but intersects the surface, it won’t come back around the dotted side of the ellipse. Hopefully.

Now here’s the minimum energy escape orbit:

http://members.xoom.com/ffungo/trashescape.gif

You’ll see that it’s a parabola with its apex at earth’s orbit. It’s a higher-energy orbit, so the trashball has to increase speed.

Now here’s the parking orbit I was talking about:

http://members.xoom.com/ffungo/parkingorbit.gif

As you can see, if you want to go faster, you go when all your velocities are pointing the same way. If you want to go slower, you go when they partially negate each other. The energy it takes to bump the trashball up into the escape orbit, then, is smaller because you get the additive effects of all the orbital velocities depicted. For the elliptical trash-to-the-sun orbit, you have to expend too much energy to slow down to the elliptical orbital velocity.

How’s that?

They say I got the power, because I got the monkeys.
They are WRONG! I got the power because I am not afraid to let the monkeys loose.

20

Yikes! Looks like Xoom has protection against outside referers.

Point taken. I confess I was conceptualizing the Sun as a point.