Orbital Mechanics

Hi Spacecowboy,

I see 2 problems with your reply.

1 SuperShuki is not planning on thrusting against the Earth’s motion, he is planning on thrusting directly at the sun. The idea that this would work at all is the misconception that I am trying to debunk, unsuccessfully it would seem.

2 The term “decaying orbit” really only refers to satellites in LEO. Such an orbit is continuously loosing energy from drag in the Earth’s upper atmosphere. This would not apply to an object in an independent orbit around the Sun.

If the Sun and Earth started at rest with respect to each other then gravity would cause them to come crashing together, even if there was no other matter in the universe, right?

The reason that the earth isn't getting closer to the sun (i.e., that it isn't moving) is that the forces are equal. But the fact that there is a countervailing force to that of gravity (i.e. inertia) does not mean that the earth is moving in respect to the sun. Since there is no change in location, the earth does not move.
To directly answer your question, therefore: yes, if there were no other forces present, gravity would cause the two objects to come crashing together. But the lack of other objects doesn't mean that there are no other forces.

Which, I'm afraid, is where you're wrong.

A few points to consider (They meet seem like irrelevant points, but if you want to talk correct physics, they're important).

There are not two equal forces acting on the Earth-Sun system. There is the force of gravity pulling them together, and there is the Earth accelerating around the Sun, causing it's circular motion. While this is often called the centripetal force in high school physics, it does not in fact exist. It's merely an acceleration acting on a mass (And there IS a difference).

Since there is therefore an acceleration acting on the Earth (Accelerating it inwards), the Earth must thereforce have a velocity relative to the Sun - it's angular velocity in fact. This means that physically speaking, they are in motion relative to one another. True, there is no radial motion (Also a little incorrect, since the Earths orbit is an elipse), but there most certainly is mtion between them. If there was not, they most definitely would go crashing into one another.

Hence the circular motion equation - mv^2/r = GM1M2/r^2
Without the velocity, they would not balance. And if there is a difference in velocity, they have to be moving.

Thanks, Sev. I hate people who think they know physics and don't.

And campbelp2002: The "decaying orbit" I was talking about was due to a constant low thrust applied against the direction of motion.

Dude, what’s your sign? I am a Leo. That means that the Sun is seen in the constellation of Leo on my birthday. If you are an Aries then the Sun is seen in the constellation of Aries on your birthday. The sun moves, as seen from the Earth, against the background of fixed stars. You are assuming that you can ignore the stars and look only at the Sun from the Earth in such a way that it seems to stand still in the sky, and that the apparent lack of motion can be assumed to be the same as a real lack of motion. This does not work for the following reason.
To make the Sun stand still in Earth's sky you need to turn the direction you are looking at just the same speed as Earth orbits the Sun, but in the opposite direction. You have in fact placed yourself in a rotating coordinate system. I am looking at the Sun-Earth system from an inertial coordinate system that is not rotating or accelerating. In my inertial coordinate system, the Sun is at the origin and the Earth moves in X and Y. (Or if you prefer polar coordinates R and Theta.) The problem with a rotating coordinate system is the virtual forces (centrifugal and coriolis) that go along with it. These forces can only be calculated from the rotation rate, so the rate that the Earth revolves around the Sun is extremely important. In addition, you are making another common but invalid simplifying assumption, that the Earth’s elliptical orbit is close enough to a perfect circle to be considered as such. From the real Earth, the Sun never stands still in the sky. It gets farther and closer as Earth moves from aphelion to perihelion. It also speeds up and slows down so that your coordinate system is rotating at a variable speed. And the only way to know that speed is to do a calculation in an inertial coordinate system.
So if you throw a rock at the Sun, it behaves just like the Earth does. It gets a little closer to the Sun, stops, moves back from the Sun, stops again, moves toward the Sun again, and so on for ever. It is a complex interplay of centrifugal force, coriolis force, and the variable rotation rate of your rotating coordinate system.
To see what will really happen if you throw a rock at the Sun, use my orbit simulator:
http://home.austin.rr.com/campbelp/orbit.html
First, click the drop button to release a “dot” from the rocket. At first the dot will be hidden behind the rocket. Consider this dot as the Earth, since the rocket starts in an orbit identical to the Earth’s orbit around the sun. Then enter 1.0g and 100.0 Sec. in the thrust controls. Turn the rocket to point at the Sun and click the Fire button. At first nothing seems to change because the rocket is still right on top of and hiding the dot. After about a quarter of an orbit the two will separate enough to see them separately. Remember, the dot represents the Earth and the rocket is the object being thrown at the Sun.

Hi spacecowboy ,
I wish you wouldn’t say things like It makes some people think that a single short impulse can result in a free coasting spiral into the Sun. They totally ignore the part of what you are saying.

Those evil people. They should all be shot.

Well, I did point out "All you have to do is to keep the package losing energy at the same low rate..."

And I tried that orbit simulator of yours -- finally got it to impact after using a 0.005g burn (manual timing), and three 0.005g correction burns (oops). Ended up with several very nice parabolas, though (despite the fact that they seemed to pass close enough to the sun to turn that rocket into a crispy critter).

I usually use 1g for 2,700 seconds for a total deltaV of 27 km/s. I tried your 0.005g for 540,000 seconds and got the same result. Note that 540,000 seconds is only 6.25 days. This is essentially instantaneous for a 1 year orbit and does not constitute a spiral in my mind. The result is still a very elongated ellipse where you coast without power most of the time.

At 0.0005g (1/10 of your acceleration) it took just under 8,000,000 seconds (92 1/2 days) to hit the Sun, thrusting all the way. I had to try about 20 times to get the steering right. If you don’t keep the rocket pointed exactly against the direction of motion all the way, you miss the Sun.

By the way, notice that 0.0005g for 8,000,000 seconds is a deltaV of 40km/s, way more than the 27 needed with the high thrust method. This is because a short duration high thrust entry into a Hohmann transfer ellipse is way more efficient than a spiral powered all the way down.

Is this why NASA is famous for using the single-burn chemical rockets, as opposed to long-burn, lower-thrust methods? The low-thrust, constant-acceleration somehow always seemed like it would be more efficient, not less.

I think it is more because that is the technology they have. Certainly deep space 1 and SMART used the slow thrust method to good effect. The high ISP of ion engines offsets the inefficient transfer.

Here is a good article about transfer orbits, including low thrust (I have posted this link before) http://en.wikipedia.org/wiki/Hohmann_transfer_orbit

Do I remeber right that chemical rockets - maybe especially NASA's ones - provide fatser acceleration than io drives but less maximum velocity than ion drives? If yes then the answer to the efficiency question is local valid only - in the desired-velocity range between 0 and the maximum velocity of chemical rockets these are mor efficient where is in the desired-velocity range above the maximum velocity of chemical rockets io drives are in the lead.

Are the circumstances where the time required for acceleration is important or the bottleneck?

It's right that Smart 1 is using the advantage of ion drives to be able to work for very long periods of time - so time of mission or consumation of proppellent may be a criterion too.



Dipl.-Volkswirt (bdvb) Augustin (Political Economist)

Actually, the particular type of efficiency that we were talking about in this case was mass-to-energy conversion efficiency: how much of a payload of fuel you would have to carry to get yourself to a specific point.

The lower the delta-Vee, the shorter and lower-thrust the burn. A single, high-thrust burn is more efficient than a long, low-thrust burn because the resultant delta-Vee is much lower -- in this case, 27 to 40 km/s.

However, the newer very-low-thrust engines, such as ion engines, have an insanely high Isp, which is the amount of thrust that they can get out of a kilogram of fuel. Chemical rockets have a much lower Isp, and can only make short, high-thrust burns. Theoretical fusion drives have an Isp that's somewhere in the middle, and are able to make burns ranging from fairly-low-thrust (maneuvering type burns) to very very high-thrust (you don't wanna know how many g's one of these babies can put out).

And yes, you're right: chemical rockets have a fairly low top speed (but they can reach that top speed pretty fast), while ion drives can approach the speed of light (after a few centuries). My pet fusion drives have a top speed of about 0.2c, and can accelerate pretty reasonably.

Now the tricky part for the engineers is to figure out which engines are best for which applications, and if they have the ability to mount them on the vehicle.

Sort of, but that is an over simplification. It would be better to say that ion drives reach the same velocity as chemical drives while using less propellant.

Ion drives have a very high exhaust velocity but a very low exhaust mass flow rate. The result is low thrust but high efficiency. Chemical rockets have a low exhaust velocity but a high mass flow rate. The result is high thrust but low efficiency. Both kinds of rocket could, in theory, reach any speed. The chemical rocket would have to use more total propellant but would reach the speed in a very short time. The ion rocket would use less total propellant but take a long time to get up to speed.

That is assuming no gravity. If the rockets are fighting gravity, then the low thrust rocket suffers a larger penalty associated with "gravity drag". The most extreme example is launch from the ground. The chemical rocket suffers a small gravity penalty and the Ion rocket never moves because it's thrust is less than it's weight. But even in orbit it can be shown that there is still a gravity drag effect that is minimized if the acceleration of the rocket is much higher than the acceleration of gravity.

In theory, if the ion engine mass flow rate could be high enough, it would have the same or even higher thrust than a chemical rocket. Engineers can't to do that with current technology, but at least in theory it is possible.