A spacecraft drifting through space...?

Question

A spacecraft drifts through space at a constant velocity. Suddenly, a gas leak in the side of the spacecraft gives it a constant acceleration in a direction perpendicular to the initial velocity. The orientation of the spacecraft does not change, so that the acceleration remains perpendicular to the original direction of the velocity. What is the shape of the path followed by the spacecraft in this situation?

parabola, circular, or linear?

Answer 1

Agree with previous answer. For extra credit, give the scenario for all three possible answers.

If it was a single jet of gas, PSSSST ! and then it stopped, it would change the direction ONE TIME in a straight line vector.

A constant jet of gas, means constant "pressure" in the perpendicular direction , means circular. Instant by instant, you can picture the spacecraft being "pushed" to one side by a constant finger. always psst. capsule will get pushed to the side by psst force / mass of spacecraft.
Perpendicular changes after each PSST toa new perpendicular so it ends uop as a circle.

But what if the hole gets larger and larger! First it's
Psst then Psssst then pssssssst the gas jet gets stronger and stronger (so you have an accelerating perpendicular pressure) you get a parabolic path.

Because your first deviation is
Psst
Psst+Psssst
Psst+Psssst+pssssssst
Psst+Psssst+pssssssst+pssssssssssssssssst

Answer 2

Circular. It might be a very large circle (like planet orbital size) but it is circular.

Note: this problem assumes no other mass-bodies are in the vicinity, otherwise all "bets" are off as to what the shape of the path is.

EDIT (following day): I can think of a parallel example: What if, instead of a leak causing perpendicular acceleration, that there is a large mass causing contant gravitational acceleration perpendicular to the satellite. What kind of motion do you have then? You call it an orbit -- it is basically circular.

RE-EDIT: I re-read the question. I read the word "orientation" as "attitude" and failed to notice that the acceleration is always perpendicular to the *original* velocity direction (which implies a vectored thrust, and not a true leak). So the correct answer is parabolic.

.

Answer 3

Chablisah, the craft has constant forward velocity, and constant perpendicular acceleration. This would cause it to gain lateral speed, and it would follow a parabolic route.

For instance, let's say it has 100m/s forward velocity (on x-axis for example) which does not change, and 10m/s^2 lateral acceleration (on y-axis). With each passing second, the lateral distance it travels would increase. After 10 seconds, it distance it travels would be equal in both directions, and in, say, a minute, it will travel more distance on the y-axis direction. The resulting route would be parabola.

Don't be confused by other answers claiming that the route is circular, it would not be circular as the orientation of the craft doesn't change. That means acceleration is always on the y-axis. If the craft rotated however, acceleration would change directions with each passing moment, and the trajectory would be a circle. But as this is not the case, the path is parabolic.

Hope this helps.. :)

Answer 4

The shape is a parabola, the velocity increasing at a constant rate in a direction perpendicular to the original path because of the constant acceleration. The velocity in the original direction of travel does not change, meaning that the spacecraft cannot travel in a circle. Because the acceleration at right angles to the original direction is constant, the distance traveled since the acceleration began is proportional to the square of the time interval. Plotted against the distance traveled in the original direction, which is a linear function of the time interval, the result is a parabola.