# Will it come back here?

1. May 4, 2005

### darkar

Let say u can fire a missile vertically, and it will only return to ground after 20 mins, will the missile hit right on where it was fired?

P/s: Assuming there is no resistance.

2. May 4, 2005

### whozum

If no wind resistance, yeah.

3. May 5, 2005

### Pengwuino

Sure will. And it'll land completely vertically too

4. May 5, 2005

### PeteSF

If you fire it from one of the Poles, yes. Otherwise, no.

Coriolis...

5. May 5, 2005

### whozum

Pete, can you explain your position?

The coriolis effect diminishes when neglecting wind resistance, and also according to this site is zero at the equator, not the poles:

http://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/fw/crls.rxml

6. May 5, 2005

### Meir Achuz

The angular momentum of the missile is conserved.
$$L=mr^2\omega$$.
As r increases, $$\omega$$ will become smaller.
The missile will land to the West of you., except at a pole, as Pete said.

Last edited: May 5, 2005
7. May 5, 2005

### whozum

Can you define your variables? mr^2 represents the moment of inertia which doesnt change during the course of flight, so I dont see why any of this should happen.

Also close your tex tags with a / not \

8. May 5, 2005

### DaveC426913

If you neglect air resistance, this can be seen as an orbital mechanics problem.

The missile's initial trajectory is the sum of it upward boost, plus its eastward velocity imparted by the rotation of the Earth.

The moment its rocket shuts off, it is in orbit about the Earth's centre of mass. The orbit is elliptical.

When it reaches the Earth's surface on the return part of its orbit, 20 minutes later, the Earth will have rotated by 5 degrees.

9. May 5, 2005

### Meir Achuz

My r was the distance from the center of the Earth, which increases as the rocket goes up.

10. May 5, 2005

### whozum

Since v < v_esc, it doesnt breach the atmosphere and it remains with the earth, its rotating along with it, isnt it? The same reason a helicopter doesnt land west of where it started while hovering in teh same place?

11. May 5, 2005

### DaveC426913

The initial post clearly indicates discounting air reisistance. This post ws a waste of time and space.

12. May 5, 2005

### whozum

So your saying BECAUSE theres no air resistance the rocket will land to the west?

If the space is bothering you feel free to delete the post, but I'm sorry if I wasted 8 seconds of your life reading that ;)

13. May 5, 2005

### PeteSF

Hi whozum,
Yes, that's right. In this case, air resistance (if the air is moving with Earth, ie no crosswind) helps to keep the rocket over the launch pad.

I'm a bit fuzzy on the details of Coriolis, but I think it works differently for North-South motion (zero at Equator, max at Poles) that for vertical motion (zero at poles, max at Equator).