# Outer space shuttle movement

So this was a test question, I got the wrong answer, now I know why, but I'm not sure which is the good answer

## Homework Statement

A spaceship is flying in outer space, engines off. At a certain point A in space, the spaceship starts drifting sideways with a constant speed and in a straight line until it reaches a distant point B in space.

## Homework Equations

Which of the forces below may have caused the spaceship to move the way it did between points A and B?
F1: A force in the direction of motion exerted by some planets or other celestial objects
F2: A force in the direction of motion due to the original thrust of the spaceship
F3: An internal impulse developed gradually by the spaceship as it moves from A to B

A. F1.
B. F2.
C. F3.
D. Either one or a combination of the above three forces.
E. None. The spaceship can move the way it did between A and B without being driven by any internal or external force.

## The Attempt at a Solution

I first chose answer A, I wasn't paying attention. Now I know that an attraction force (F1) would at least be the same from point A to B so there would be acceleration an thus no constant speed. F2 and F3 aren't good as well. Answer D doesn't seem correct, so I've got option E left. However I cannot understand how this would be possible. Could someone give an explanation? Or maybe it isn't E...?

Thank you!

## Answers and Replies

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jhae2.718
Gold Member
If an object moves at constant velocity, what is the net acceleration? Then, using $$\vec{F}=m\vec{a}$$, what must the net force be?

Edit: it's constant speed, not velocity. Misread the initial post...the above doesn't necessarily apply...

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Thank you for your answer.
I know that acceleration is 0, and that there is no force acting on the shuttle. But then what makes it change its direction at point A?

jhae2.718
Gold Member
Actually, above I should have stated that a constant velocity means that there is no acceleration (I've since fixed that.). In cases of circular motion for example, speed is constant and velocity is not.

Does the problem state anything about the initial conditions of the spaceship other than that the engines are off?

No, unfortunately it doesn't say anything except that it moves with its engines off. Then something happens and starts moving in a straight line, with constant speed to point B.

There has to be a force that causes a change in the movement. However, looking back at the problem, the question is "Which of the forces below may have caused the spaceship to move the way it did BETWEEN points A and B?". Yeah, I think they are interested only in the movement from A to B, that means no force. Hmmm, tricky question. Thank you anyway for your help! I would go for E, if someone has a different opinion, let me know.

jhae2.718
Gold Member
Let's examine each of the options. The speed is constant, and the spaceship moves in a straight line, so I'll make the simplifying assumption that the spaceship moves in 1-D. Speed is the magnitude of the velocity vector. That means, if speed v is constant, velocity is +/-v. So, in this case, we should be able to extend that to mean velocity is constant. (Instantaneously changing velocity from v to -v would require infinite acceleration.)

For F1, a planet/etc. exerts an attractive force on the space shuttle. This force is $$\vec{F}_g=-\frac{GMm}{r^2}\hat{r}$$, where the negative sign indicates attraction and r-hat is the unit vector in the direction of attraction. Now, this means that the acceleration is proportional to the inverse of the distance squared. This is a variable force, which will impart a variable acceleration. Therefore, the spaceship could not move at a constant speed.

For F2, the original thrust of the spaceship will not remain as a force after the engine is off. The engine could have exerted a force in the direction of motion while it was on, but after it is off it exerts no force.

For F3, internal forces won't affect the motion of the spaceship. (Recall that impulse is just the time integral of force: I=∫F dt.)

It won't be a combination of the three, since there is no force F2, and internal forces will not affect motion. The sum of forces must be zero based on our above analysis, so F1 must have a magnitude of zero.

Therefore, no forces acting on the system is the best answer, and we come to the conclusion that the initial speed of the spaceship must have been in the direction of travel.

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