# Forces question - acceleration of a rocket

1. Mar 23, 2006

### QueenFisher

A simple rocket flying towards the moon has a constant thrust from its engine. Will the acceleration remain constant? If not, how will it vary with time?
this is a question i've been given to think about. obviously i don't want any outright answers, can anyone tell me if i'm going in the right direction here?

i think that as it gets further away from the earth, the gravitational attraction between the rocket and the earth becomes less. as the acceleration depends on the resultant force, as it gets further away, the acceleration will increase. at the equilibrium point, will it have zero acceleration?
after the equilibrium point, the gravitational attraction between the rocket and the moon will be increasing as the rocket approaches the moon, so the reultant force will be increasing, so the acceleration will be increasing.

any comments would be great

2. Mar 23, 2006

### Hootenanny

Staff Emeritus
Sounds like a very lucid explanation to me

3. Mar 23, 2006

### Chi Meson

Also consider what happens to the mass of the rocket as it uses its fuel.

4. Mar 23, 2006

### QueenFisher

as in, as it uses more fuel, it's mass will be less, so the gravitational attraction will be less? does that mean it can accelerate at a faster rate?

also, is the physics ok in my first post?

5. Mar 23, 2006

### Hootenanny

Staff Emeritus
You've got it!

Your post sounds good to me

6. Mar 23, 2006

### Chi Meson

the thrust force of the rocket remains constant. The mass decreases. even without consideration of the gravitational force, the acceleration will increase due to Newton's second law, a=F/m.

In your OP, what did you mean by "equilibrium point"? The net zero gravitational point between Earth and Moon? The acceleration won't be zero there (Rocket is still thrusting, or is it?).

7. Mar 23, 2006

### Hootenanny

Staff Emeritus
I think she may have meant on take off. That was my take on it anyway.

8. Mar 28, 2006

### QueenFisher

nah i meant where the earth's and the moon's gravitational forces can be considered to cancel each other out. i think it's at that point that there will be a constant acceleration...as opposed to constantly changing acceleration?

9. Mar 28, 2006

### Chi Meson

(Thread comes back from the dead)

At the earth-moon equilibrium pont, the gravitational force will not contribute to the rocket's acceleration, but...

All the way to, through, and beyond this point the Earth will pull less and less and the Moon will pull more and more. So the acceleration of the rocket will continue to increase as it gets closer to its destination.

The fact that the mass is decreasing the entire time will be a more significant factor to cause an increase in acceleration (as long as the thrust force is constant).

10. Mar 29, 2006

### QueenFisher

does that mean that the rocket's acceleration is increasing at a greater rate when it is losing mass due to fuel consumption that if it were not?

11. Mar 29, 2006

### Hootenanny

Staff Emeritus
Yes, remember Newton's law $F = ma$, so the same force will acclerate an object of a lower mass faster.

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