# Escape Velocity Formula

Gold Member
Let's say I have an object orbiting the Sun in a circular orbit with an orbital velocity of 30 km/s. If I want to accelerate prograde into a hyperbolic orbit, and I'd like my velocity relative to the Sun to be 1 km/s at infinity, what is the formula I'd use to figure out how much delta v in the prograde direction I'd have to apply? I believe the formula for escape velocity is $circular velocity * sqrt{2}$, but I want to know how much further I must accelerate to have 1 km/s of extra velocity when the rocket has distanced itself from the Sun.

Also, how do I get the root symbol in the tex tags?

Janus
Staff Emeritus
Gold Member
You would have to accelerate 1 km/sec more.

The root function for squareroot is \sqrt{n} the radical sign will be placed over n like this:
$$\sqrt{2}$$

or
$$\sqrt{\frac{2GM}{R}}$$

Gold Member
Never mind... I figured it out. $$vescape = \sqrt{2}*vcircular$$
$$vrequired = \sqrt{vescape^2 + vinfinity^2}$$

edit... to change to TEX format. I love these TEX things. Thanks Janus.

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