# How rockets take curved paths in space (absent gravity)

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1. Oct 6, 2015

### Emspak

This might have been answered before but it's something that has been bothering me.

A rocket in space will move in a straight line. If I apply thrust, it still moves in a straight line unless I apply the thrust in a different direction. So unless I have rocket nozzles attached to the side, applying a thrust vector in some other direction, my rocket will go in a straight line -- well and good.

Now, here's what I wasn't sure about. If said rocket is moving ballistically -- just tooling along in a straight line after I apply some thrust (say I do a burn for 1 second). Now I have a nozzle at the end of the rocket, towards the back, facing 90 degrees away from my main engine.

What happens when I fire the small engine near the end, for just a second or two?

Would the rocket start rotating and continue on it's original vector? So it continues n the path it had before, but in a little while it will be facing backward?

Would the rocket start moving along another vector at right angles to my original, ballistic path, so that we're still moving in a straight line, but now instead of straight along my original path it's a straight line vector that's the sum of the small, right-angle engine's nudge and the original ballistic trajectory? (I know, both trajectories are ballistic strictly speaking, as they aren't under continuous thrust).

Does the answer depend on how far off center my 90-degree-directional nozzle is? My intuition says yes, that if it's off-center the rocket will start rotating because whatever the rocket is doing (as long as it's not accelerating) the small thruster is moving one end of my rocket, but since the end is attached to the center of mass and there's no reason for that to move -- it will stay where it is "stationary" relative to the end of the rocket.

But anyway, I was curious, because I was thinking about how to make a rocket take a curved path absent a local gravity field -- imagine being in deep space somewhere and you want to travel in a curved path. (Maybe you want to turn around because you forgot your keys or something and need to pick up a quart of milk at space A&P on the way home :-) )

2. Oct 6, 2015

### HallsofIvy

Not quite. When a force, such as a rocket engine, is applied along a line that does NOT go through the center of mass (the main rocket will of course apply thrust through the center of gravity) two things will happen. The rocket will start to turn and there will be an acceleration in the direction of the thrust. If you want only turning, you will have to fire two rocket engines, in opposite directions, place equi-distant from the center of mass.

Yes, together with the rotation.

Yes, depending on how far off the center of mass the nozzle is.

To have a true "curved path", rather than a series of lines that approximate a curve, you would have to had a continuously varying engine blasts.

3. Oct 6, 2015

### rcgldr

Usually the main rocket nozzles are adjustable (they can pivot a small amount using a gimbal like arrangement). They need to be adjustable in order to avoid a rocket turning due to changing mass within the rocket (like the fuel). To turn, the nozzles could just be adjusted.

http://www.aerospace.org/education/stem-outreach/space-primer/solving-problems

4. Oct 6, 2015

### Janus

Staff Emeritus
You could do it this way. With the two small nozzles at the two ends of the rocket, start it rotating end to end. When your main engine is pointing at 90 degrees to your initial velocity, fire your main engine( you may have to continually be making adjustments to maintain a steady rate of rotation) and continue firing your engine until you have rotated another 180 degrees and then shut off the main engine. Let your ship continue rotating for 90 degrees and stop your rotation with the small nozzles.

How hard you have to fire your main engines depends on your initial velocity and how much time you want to spend turning around. For example, if you are moving at 1 km/sec and want to make the turn in 5 min, you would need to thrust the main engine at ~1g for the entire turn to get a semi-circular trajectory with a radius of ~95 km. Making a tighter turn would require a higher thrust and faster rotation.

However, this is a bit wasteful, as you could get the same end result (turning around and heading back at 1 km/s) by letting your ship rotate 180 degrees, stop the rotation and then fire your engine at the same thrust as above for only 3.2 min.

5. Oct 6, 2015

### DaveC426913

This, I believe:

You have two types of propulsion: main thrust and attitude.
Main thrust is through the long axis of your craft.
Attitude adjusters are as far to ends and as far outboard as practical for best leverage.

If you want to change course, you:
1] turn off your main engine
2] Fire a burst from your attitude jets to start the craft spinning. (Duration of burn dependent on how fast you wish to turn / what craft and occupants can withstand).
3] When spacecraft is pointing 90 degrees to its direction of travel, fire another burst.
5] Optionally, use attitude jets again to point craft in direction of travel.

There are a few other scenarios to cover other course changes, such as a direct reversal, but the upshot is there's no reason for curved paths. (A curved path means you are using your attitude thrusters constantly. Don't.)

You are either burning main engines, adjusting attitude or coasting - they're essentially mutually-exclusive. Not entirely exclusive - you can overlap a main burn with an attitude adjustment, but the overlap will be small (long main burns, interrupted with very short attitude bursts). The functions of the two burns are distinct.

Essentially, interplanetary travel will be alternating thrust turn thrust turn.

6. Oct 6, 2015

### Janus

Staff Emeritus
A lot depends on what type of course change you want to make and how much fuel you want to use up doing so.

Using your method, to make a 30 degree course change while moving at 1 km/sec would require a total delta v change of 577 m/s leaving you with a final velocity of 1.155 km/sec after the maneuver.

If however, you wish to save fuel, you can let your ship continue to turn for another 15 degrees before stopping the rotation and firing the main engine, this will give you the same angular deflection with only a Delta v change of 517 m/s (and leaves the magnitude of your velocity unchanged.)

The larger the deflection angle, the larger the difference between the two methods.

7. Oct 6, 2015

### DaveC426913

Yeah, several different scenarios. Too many to go into unless we were of a mind.

Yup. Mine results in a higher velocity toward target once done. Maybe preferable, maybe not.

Basically, what we're doing here is vector addition.

8. Oct 6, 2015

### Janus

Staff Emeritus
Yeah. sometimes just getting to the right point isn't enough, you have to get there at the right moment too. Say you are going to use a gravity-slingshot to get you to your final destination. If you don't arrive at the slingshot point at the right time, you won't get the right boost in the right direction. So any course correction has to take into account not only how it effects the direction but also the arrival time.

Or let's take another hypothetical scenario: Assume we have a small asteroid heading towards the Earth. Somehow we have come up with a means of deflecting it (buried thermonuclear device etc.). The asteroid is moving at 10 km/sec, and we are capable of giving it a 1 km/sec "kick". Where is the best point to apply the kick to get the maximum angle of deflection? It works out to be ~ 84.29 degrees from the velocity vector of the asteroid.