# Parabolic trajectory of a rocket

1. Jan 6, 2009

### putongren

Why is the trajectory of a rocket always parabolic if a rocket launches straight up in the air perpendicular to the ground? Doesn't a rocket just drop straight down back to the launch pad? I think the rocket lands away from the launch pad depending on the speed of the rocket.

2. Jan 6, 2009

### Staff: Mentor

I would consider that to be a special case of a parabola or a limit condition. And it does drop straight down (ignoring the earth's rotation).

3. Jan 7, 2009

### putongren

Russ,

What do you mean by limiting condition? So a rocket like an ICBM lands far away because of thrust vectoring?

4. Jan 7, 2009

### Staff: Mentor

A limit condition is a simplified special case - like a circle is to an ellipse.

And now I see your confusion - real rockets on launch pads tend to start off straight up. Yes, these rockets are steered. They don't end up on a ballistic (parabolic) trajectory until after their engines are stopped.

5. Nov 21, 2009

### IPhO' 2008

If v of the rocket is high. But v < $$\sqrt{\frac{2GM}{R}}$$
where M is the mass of Earth
R is the radius of Earth
The trajectory of the rocket is a part of ellipse because g is change accordingly to h (likes the trajectory of planet). One focus of this ellipse is the center of earth.