Why is a rocket trajectory curved after launch?

What goes up must come down, and gravity has a big part to play in forming the beautiful parabolas followed by rockets after lift-off.

2nd October 2017
Why is a rocket trajectory curved after launch? © SpaceX

© SpaceX

Asked by: Fred Wilhelm, US

Students have long been taught that all projectiles follow a curved path known as a parabola. The explanation is that as they fly, they cover distance both horizontally and vertically – but only the latter is affected by the force of gravity, which bends the path of the projectile into a parabola.

For long-range rockets, things are more complex. For example, air resistance must be taken into account. But even ignoring that, a projectile doesn’t really follow a parabola – because the Earth isn’t flat. This means that gravity doesn’t simply pull objects straight back down. Instead, it pulls them towards the centre of the Earth, whose direction changes as the projectile moves further down-range, away from the launch site. Detailed calculations then reveal that the true trajectory is not a parabola, but part of an ellipse. 

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