Parabolic trajectory of a rocket

[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.

 

[russ_watters]

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).

 

[putongren]

Russ,

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

 

[russ_watters]

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.

 

[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.