# Why escape velocity? **URL:** \ **Category:** Factual Questions\ **Created:** [August 1, 2002, 2:35am UTC](https://boards.straightdope.com/t/why-escape-velocity/121807 "2002-08-01T02:35:40Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Arcite](https://avatars.discourse-cdn.com/v4/letter/a/67e7ee/32.png) [@Arcite](https://boards.straightdope.com/u/Arcite)\ **Post date:** [August 1, 2002, 2:35am UTC](https://boards.straightdope.com/t/why-escape-velocity/121807/1 "2002-08-01T02:35:40Z")
According to [this page,](http://www.howstuffworks.com/satellite3.htm) “A rocket must accelerate to at least 25,039 mph (40,320 kph) to completely escape Earth’s gravity and fly off into space.” I’ve never understood this. Why must a body be traveling at a certain velocity in order to escape the gravity of another body? Going by my pathetically poor memory of high school physics, I would think you’d need “escape work” instead–that is, a force applied over a certain distance. Why does it matter how fast you travel when leaving the earth? As long as you’re moving away from it at any speed, you’d break free eventually, right? Consider: supposed I invent a miraculous engine that can generate a broad range of thrust, from miniscule through prodigious, while consuming only a tiny amount of fuel (so that the weight of fuel doesn’t enter into the equation.) Couldn’t I blast off, accelerate to, say, 100 mph, then just keep moving at 100 mph until I leave the solar system? Sure, it would take many lifetimes to leave the solar system at only 100 mph, but, hypothetically speaking, wouldn’t it be possible? ---
**Author:** ![DarrenS](https://avatars.discourse-cdn.com/v4/letter/d/977dab/32.png) [@DarrenS](https://boards.straightdope.com/u/DarrenS)\ **Post date:** [August 1, 2002, 2:52am UTC](https://boards.straightdope.com/t/why-escape-velocity/121807/2 "2002-08-01T02:52:10Z")
Welcome to the SDMB, Arcite…good, well-worded question. I found the following [derivation](http://theory.uwinnipeg.ca/mod_tech/node58.html) of the equation for escape velocity, which explains where the formula comes from. Intuitively, and in non-mathematical terms, I have trouble explaining and understanding why you couldn’t just travel at 100 mph continuosly and get off, whatever the E.V. ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [August 1, 2002, 2:54am UTC](https://boards.straightdope.com/t/why-escape-velocity/121807/3 "2002-08-01T02:54:28Z")
IANAP, but it is precisely because rockets do not continually fire that escape velocity is important. Rockets bring a body up to a speed. Below escape velocity, a body which does not have a constant force working on it will eventually be tugged back to earth. As the space elevator concept shows, any speed will indeed remove you from the earth’s surface as long as force is being continually applied. I see no reason why this could not continue indefinitely. But that is not the way rockets currently work. ---
**Author:** ![scr4](https://avatars.discourse-cdn.com/v4/letter/s/59ef9b/32.png) [@scr4](https://boards.straightdope.com/u/scr4)\ **Post date:** [August 1, 2002, 2:56am UTC](https://boards.straightdope.com/t/why-escape-velocity/121807/4 "2002-08-01T02:56:06Z")
You are right. The escape speed is how fast you have to throw something so it never comes back down to earth. It doesn’t apply to a spacecraft which can run its engines continuously. But in reality, most spacecraft use rocket engines which have large thrust and short burn time. You fire the rockets briefly to achieve escape speed, then coast all the way to the destination. That’s how the Apollo spacecraft worked, as well as most interplanetary probes. ---
**Author:** ![DarrenS](https://avatars.discourse-cdn.com/v4/letter/d/977dab/32.png) [@DarrenS](https://boards.straightdope.com/u/DarrenS)\ **Post date:** [August 1, 2002, 2:59am UTC](https://boards.straightdope.com/t/why-escape-velocity/121807/5 "2002-08-01T02:59:00Z")
Also found [this](http://www.physlink.com/Education/AskExperts/ae158.cfm). > [@](#): > > If you throw an object straight up, it will rise until the the negative acceleration of gravity stops it, then returns it to Earth. Gravity’s force diminishes as distance from the center of the Earth increases, however. So if you can throw the object with enough initial upward velocity so that gravity’s decreasing force can never quite slow it to a complete stop, its decreasing velocity can always be just high enough to overcome gravity’s pull. The initial velocity needed to achieve that condition is called escape velocity. ---
**Author:** ![xash](https://avatars.discourse-cdn.com/v4/letter/x/c6cbf5/32.png) [@xash](https://boards.straightdope.com/u/xash)\ **Post date:** [August 1, 2002, 3:05am UTC](https://boards.straightdope.com/t/why-escape-velocity/121807/6 "2002-08-01T03:05:13Z")
resident newtons will be here soon… v = sqrt(2GM/r) meanwhile, here’s something to confuse you further 😛 [http://www.perpendicular.org/papers/escape.htm](http://www.perpendicular.org/papers/escape.htm) _on preview… damn these guys are fast! what’s the escape velocity of the SDMB by which you guarantee being the first to reply to a new thread ?_ p.s. excellent question… ---
**Author:** ![xash](https://avatars.discourse-cdn.com/v4/letter/x/c6cbf5/32.png) [@xash](https://boards.straightdope.com/u/xash)\ **Post date:** [August 1, 2002, 3:12am UTC](https://boards.straightdope.com/t/why-escape-velocity/121807/7 "2002-08-01T03:12:03Z")
also, from this site: [http://www.bu.edu/satellite/classroom/lesson05-1.html](http://www.bu.edu/satellite/classroom/lesson05-1.html) > [@](#): > > If a rocket moves faster than 11.5 km/sec (called the escape velocity), it will leave the Earth’s gravity forever. The space shuttle and all Low Earth Orbiting (LEO) satellites move at a speed of approximately 8 km/sec (5 miles per second). so it seems that a space shuttle at 8km/sec (faster than your proposed 100mph) will still not leave the earth’s orbit due to the gravitational attraction, but will instead orbit the earth… so maybe a rocket doing 290mph would escape the earth ? ---
**Author:** ![xash](https://avatars.discourse-cdn.com/v4/letter/x/c6cbf5/32.png) [@xash](https://boards.straightdope.com/u/xash)\ **Post date:** [August 1, 2002, 3:16am UTC](https://boards.straightdope.com/t/why-escape-velocity/121807/8 "2002-08-01T03:16:08Z")
> [@](#): > > \*Originally posted by xash \* > \*\*so maybe a rocket doing 290mph would escape the earth ? \*\* nooo nooo wait what am i saying! :eek: … if 11.5km/sec escapes the earth, and 8km/sec orbits the earth … what happens to … say… 10km/sec things ? ---
**Author:** ![Achernar](https://avatars.discourse-cdn.com/v4/letter/a/e274bd/32.png) [@Achernar](https://boards.straightdope.com/u/Achernar)\ **Post date:** [August 1, 2002, 3:30am UTC](https://boards.straightdope.com/t/why-escape-velocity/121807/9 "2002-08-01T03:30:30Z")
It goes into a higher orbit. ---
**Author:** ![Race\_Bannon](https://avatars.discourse-cdn.com/v4/letter/r/5f8ce5/32.png) [@Race\_Bannon](https://boards.straightdope.com/u/Race_Bannon)\ **Post date:** [August 1, 2002, 3:30am UTC](https://boards.straightdope.com/t/why-escape-velocity/121807/10 "2002-08-01T03:30:37Z")
Exapno and scr4 have it right. Escape velocity is the speed at which an object will leave the earth forever, with no further application of thrust. Think of it this way, if you throw something up in the air, you know that the faster its speed (when it leaves your hand, ignore the atmosphere) the higher it will go. If you throw it up at a speed less than escape velocity, it will go slower as it goes higher, but will eventually turn around and fall back down, or be in a closed orbit. If you throw it at a speed greater than escape velocity, it will still go slower as it goes up, but will never ever turn around, or be in a closed orbit. Generally speaking, escape velocity varies with the distance from the center of the earth. If you’re already up in a closed orbit (like on the space shuttle) the escape velocity _from there_ is less than at the surface of the earth. ---
**Author:** ![Arcite](https://avatars.discourse-cdn.com/v4/letter/a/67e7ee/32.png) [@Arcite](https://boards.straightdope.com/u/Arcite)\ **Post date:** [August 1, 2002, 3:45am UTC](https://boards.straightdope.com/t/why-escape-velocity/121807/11 "2002-08-01T03:45:07Z")
> [@](#): > > \*Originally posted by scr4 \* > \*\*You are right. The escape speed is how fast you have to throw something so it never comes back down to earth. It doesn’t apply to a spacecraft which can run its engines continuously. > > But in reality, most spacecraft use rocket engines which have large thrust and short burn time. You fire the rockets briefly to achieve escape speed, then coast all the way to the destination. That’s how the Apollo spacecraft worked, as well as most interplanetary probes. \*\* Oooooooohhhhhhh… now I get it! Thanks. I think that answers the question perfectly. ---
**Author:** ![JS\_Princeton](https://avatars.discourse-cdn.com/v4/letter/j/57b2e6/32.png) [@JS\_Princeton](https://boards.straightdope.com/u/JS_Princeton)\ **Post date:** [August 1, 2002, 4:55am UTC](https://boards.straightdope.com/t/why-escape-velocity/121807/12 "2002-08-01T04:55:42Z")
You always reach an escape velocity when you leave a gravitational field. No matter how long it takes you to accelerate to it. ---
**Author:** ![RM\_Mentock](https://avatars.discourse-cdn.com/v4/letter/r/e274bd/32.png) [@RM\_Mentock](https://boards.straightdope.com/u/RM_Mentock)\ **Post date:** [August 1, 2002, 6:05am UTC](https://boards.straightdope.com/t/why-escape-velocity/121807/13 "2002-08-01T06:05:43Z")
JS Princeton And when do you leave a gravitational field? ---
**Author:** ![Bryan\_Ekers](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bryan_ekers/32/183_2.png) [@Bryan\_Ekers](https://boards.straightdope.com/u/Bryan_Ekers)\ **Post date:** [August 1, 2002, 8:01am UTC](https://boards.straightdope.com/t/why-escape-velocity/121807/14 "2002-08-01T08:01:48Z")
> [@](#): > > \*Originally posted by RM Mentock \* > And when do you leave a gravitational field? As soon you have evidence of adultery. ---
**Author:** ![Rhapsody](https://avatars.discourse-cdn.com/v4/letter/r/9de0a6/32.png) [@Rhapsody](https://boards.straightdope.com/u/Rhapsody)\ **Post date:** [August 1, 2002, 10:59am UTC](https://boards.straightdope.com/t/why-escape-velocity/121807/15 "2002-08-01T10:59:41Z")
think of it this way. Say you have a 1 lb ball on a string that will break at 20 lbs. now you swing the ball over your head until you have it going at 20g’s at this point the string breaks and the ball flys away. The string represents gravity. Now if you take that same ball and shoot it out of a gun at that same speed the string will break and the ball will continue forward until something else stops it. 20g’s could be considered the “escape velocity” of the ball/string system. If you don’t reach that speed the “string” will keep the ball in the system. ---
**Author:** ![sailor](https://avatars.discourse-cdn.com/v4/letter/s/a587f6/32.png) [@sailor](https://boards.straightdope.com/u/sailor)\ **Post date:** [August 1, 2002, 11:50am UTC](https://boards.straightdope.com/t/why-escape-velocity/121807/16 "2002-08-01T11:50:39Z")
(Ignore atmospheric friction etc) You throw a ball up and it comes down again. The more speed you give it up, the higher it goes and the longer it takes to come down. There is a certain speed at which it will not return and this is called escape velocity. Escape velocity diminishes as you go farther away from the surface. In fact, if you shoot a ball up with escape velocity, as it goes up and slows down it will have escape velocity for each altitude. Escape velocity is that which gives sufficient kinetic energy to escape. Orbits are a different thing alltogether. If you throw something _up_ with less than escape velocity it will fall back down, it will not go into orbit. Escape velocity refers to the vertical component while to put something in orbit you need a tangential component. ---
**Author:** ![Aro](https://avatars.discourse-cdn.com/v4/letter/a/b3f665/32.png) [@Aro](https://boards.straightdope.com/u/Aro)\ **Post date:** [August 1, 2002, 12:11pm UTC](https://boards.straightdope.com/t/why-escape-velocity/121807/17 "2002-08-01T12:11:00Z")
> [@](#): > > \*Originally posted by RM Mentock \* > \*\*JS Princeton > > And when do you leave a gravitational field? \*\* you never do, the force just becomes negligible. Newton states that _"every particle attracts every other particle in the universe with a force that is directly proportional to the product of their masses, and inversely proportional to the square of their distances apart”_ ---
**Author:** ![Shagnasty](https://avatars.discourse-cdn.com/v4/letter/s/9dc877/32.png) [@Shagnasty](https://boards.straightdope.com/u/Shagnasty)\ **Post date:** [August 1, 2002, 12:14pm UTC](https://boards.straightdope.com/t/why-escape-velocity/121807/18 "2002-08-01T12:14:36Z")
This is one of the first questions I asked on this board too [http://boards.straightdope.com/sdmb/showthread.php?threadid=24421&highlight=escape+velocity](http://boards.straightdope.com/sdmb/showthread.php?threadid=24421&highlight=escape+velocity) The reply to mine included this from Chronos which I found interesting: > [@](#): > > \*Originally posted by Chronos \* > \*\*Sorry about this, but it’s a pet peeve of mine… Escape velocity is a misnomer. The correct term is escape speed. The difference? Velocity is a vector, and has magnitude and direction. Speed is a scalar, and does not have any particular direction. If I had a cannon with a muzzle speed of 11.2 km/s, and I shot it straight up, the cannonball would never fall back to Earth (we’re neglecting air resistance here). Now, if I took that same cannon, and aimed it exactly horizontally, the ball would _still_ never fall back to Earth. If I shot it down, provided that there were a tunnel through the Earth for the ball to travel through, the result would be the same, likewise for any angles in between. > The only reason that people call it escape velocity is because it sounds more “scientific”. \*\* ---
**Author:** ![CurtC](https://avatars.discourse-cdn.com/v4/letter/c/ce73a5/32.png) [@CurtC](https://boards.straightdope.com/u/CurtC)\ **Post date:** [August 1, 2002, 2:42pm UTC](https://boards.straightdope.com/t/why-escape-velocity/121807/19 "2002-08-01T14:42:35Z")
> [@](#): > > _sailor wrote:_ > If you throw something _up_ with less than escape velocity it will fall back down, it will not go into orbit. Escape velocity refers to the vertical component while to put something in orbit you need a tangential component. So what happens if you throw something horizontally at 26000 mph (neglecting air resistance, of course), since there’s no vertical component? ---
**Author:** ![scr4](https://avatars.discourse-cdn.com/v4/letter/s/59ef9b/32.png) [@scr4](https://boards.straightdope.com/u/scr4)\ **Post date:** [August 1, 2002, 4:03pm UTC](https://boards.straightdope.com/t/why-escape-velocity/121807/20 "2002-08-01T16:03:49Z")
**Chronos** (as quoted by **Shagnasty** ) is correct, and **sailor** ’s post is a bit misleading. Direction doesn’t matter. If you throw something horizontally at escape speed, it will never come back to the earth - just like if you threw it upwards at the same speed. [Next page](https://boards.straightdope.com/t/why-escape-velocity/121807.md?page=2)