# Does it take escape velocity to reach orbit?

I don't comprehend what is meant by "escape"

The internet gives me two meanings thus my following ambiguity:

Does escape velocity mean to reach infinitely far from the earth or to just reach orbit?

Technically the latter did "escape" from the ground

So does It take escape velocity to reach orbit?

I feel like I got a lot of things wrongs, thanks in advance!

• Are you talking about projectiles or rockets? Jan 21, 2021 at 13:52

As already mentioned by Steeven, escape velocity is the minimum velocity required for an object to forever move away from some body (to escape the body's gravitational field). It can mathematically be described by

$$v_{esc}=\sqrt{\frac{2GM}{r}}$$

where $$G$$ is the Gravitational constant, $$M$$ the body's mass and $$r$$ the distance to the center of the body. It should however be mentioned that escape velocity is only needed if there is no external force acting on the "escaping" body. This means that if you reach $$v_{esc}$$ for an infinitesimal short amount of time, you would escape the Earth's (or any other object's) gravitational field.

If, on the other hand, you keep accelerating or there is a constant force acting on you, you don't need to reach escape velocity. For example, this is the case with rockets which constantly burn engine - they don't reach escape velocity during takeoff.

On a side note, orbital velocity can be described by

$$v=\sqrt{\frac{GM}{r}}$$

(As mentioned by notovny, this formula only holds for circular orbits).

• Note that $v=\sqrt{\frac{GM}{r}}$ describes circular orbit velocity. Stable elliptical orbits exist for any combination of $v$ and $r$ where the periapsis isn't low enough to smack into the body being orbited, and $v<v_{esc}$ for the given $r$. Jan 21, 2021 at 14:57
• For all orbits, the vis viva equation relates the current orbital speed $v$ to the current orbital radius $r$ and the mean orbital radius $a$. $$v^2=GM\sqrt{\frac2r-\frac1a}$$ See en.wikipedia.org/wiki/Specific_orbital_energy for further details. Jan 23, 2021 at 16:42

The escape velocity is what is needed to escape all orbit. Meaning to escape the gravitational field. Since that field extends to infinity, this corresponds to getting infinitely far away. If you can't get infinitely far away, that is because you got caught in a (possibly very large) orbit.

So your first suggestion is correct.

Escape velocity is the minimum speed needed for a free, non-propelled object to escape from the gravitational influence of a massive body, that is, to eventually reach an infinite distance from it.

• Hello sir ,In attempt to upvote your answer I seem to have downvoted it .Could you please edit it so I can undo my mistake. Jan 23, 2021 at 15:18
• @Glowingbluejuicebox Aha, I see 🙂 Sure, I made a tiny edit. Jan 23, 2021 at 16:09
• @Glowingbluejuicebox you should be able to undo votes simply clicking on the respective button again. Jan 23, 2021 at 16:18
• @Jonas Votes get locked after 5 minutes. See meta.stackexchange.com/q/80762/334566 Jan 23, 2021 at 16:33