Ep. 318: Escape Velocity

Sometimes you’ve just got to get away from it all. From your planet, your Solar System and your galaxy. If you’re looking to escape, you’ll need to know just what velocity it’ll take to break the surly bonds of gravity and punch the sky.

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This episode is sponsored by: Swinburne Astronomy Online, 8th Light, Cleancoders.com

Show Notes

  • Poem: “High Flight” — ‘Oh, I have slipped the surly bonds of Earth…’
  • The Simpsons
  • Escape Velocity — Northwestern University
  • Newton’s Cannonball and the Universal Law of Gravitation  — University of Rochester
  • Kerbal Space Program
  • Escape Velocity on Wikipedia
  • Discussion on the Cosmoquest Forum about black hole event horizon and escape velocity
  • Transcript

    Transcription services provided by: GMR Transcription

    Female Speaker: This episode of Astronomy Cast is brought to you by Swinburne Astronomy Online, the world’s longest-running online astronomy degree program. Visit astronomy.swin.edu.au for more information.

    Fraser Cain: Astronomy Cast Episode 318: Escape Velocity

    Welcome to Astronomy Cast, our weekly facts-based journey through the cosmos. We hope you understand not only what we know but how we know what we know.

    My name is Fraser Cain. I’m the publisher of Universe Today and with me is Dr. Pamela Gay, a professor at Southern Illinois University, Edwardsville, and the director of CosmoQuest.

    Hey, Pamela. How are you doing?

    Pamela Gay: I’m doing well. How are you doing, Fraser?

    Fraser Cain: Good. Now, everybody loves your voice and, you know, I can’t argue with that.

    Pamela Gay: People love your voice too.

    Fraser Cain: Well, so the thing is, is that I was, like, talking to someone on the phone about scheduling some room for an event and someone’s like, “Are you a professional speaker or something?”

    I’m like, “Well, no.”

    Pamela Gay: Yes, yes you are.

    Fraser Cain: Well, I didn’t want to explain so I’m, like, “No.”

    “Well, you’ve got a really nice voice.”

    So, I don’t know what it is. Maybe I’ve been taking notes from you, Pamela, but this is like the first time anyone’s like, “Oh, you should, like, be in broadcast.”

    Like, “Oh, okay. Awesome.”

    Pamela Gay: But you are in broadcast.

    Fraser Cain: I know but I didn’t want to explain. Like, I do a podcast with astronomy; like, “What?”

    So, anyway, I thought that was great because everyone’s like, “Oh. I love Pamela’s voice. She should –”

    Yeah, so that was my first time and I know you’ve gotten zillions of them but – there ya go.

    So, you’re back from Poland.

    Pamela Gay: I am. I am suffering an 8-hour time change but yeah, I’m back.

    It was a great conference; met up with people from all over the globe that are working to use all means possible to engage their local populations and global populations in learning and doing astronomy. So that was really fantastic and there’s going to be blog posts coming. I was live-streaming everything using Google Hangouts on air, so I couldn’t type effectively, because if you type, you silence your hangout. So, there’s a lot of catching up to be done.

    Fraser Cain: But the bottom line is, is that if you’re interested in any way about communicating astronomy to the public which, of course, we sure are, check out all of the work that Pamela’s been doing with this latest conference. And mountains of information came out, lots of meetings, lots of video you guys recorded, lots of panels, documents. It’s gonna be a gold mine for communicating astronomy to the public.

    Pamela Gay: And we’re working in putting together a circle of astronomy communicators. So, drop me a note on Google Plus if you want to be part of the circle.

    Fraser Cain: That sounds great. And, speaking of Google Plus, of course we record Astronomy Cast live every Monday at 12:00 Pacific, 3:00 Eastern. And so, right now, we are recording this as a live Google Plus Hangout.

    So, a few ways you can find that. You can find that just on the Astronomy Cast page on Google Plus and we’ll post an event every week and you can join it there and then, of course, we’ll post the follow-up video back on Astrospheres so you can catch up.

    Alright. Well, let’s get rolling.

    Female Speaker: This episode of Astronomy Cast is brought to you by 8th Light, Inc. 8th Light is an agile software development company. They craft beautiful applications that are durable and reliable. 8th Light provides disciplined software leadership on demand and shares its expertise to make your project better.

    For more information, visit them online at www.8thlight.com. Just remember, that’s www.8thlight.com. Drop them a note. 8th Light. Software is their craft.

    Fraser Cain: So sometimes, you’ve just got to get away from it all; from your planet, your solar system and your galaxy. So, if you’re looking to escape, you’ll need to know just what velocity it’ll take to break the surly bonds of gravity and punch the sky. I hope people know what reference that is. It’s from The Simpsons – which is, it’s a little different in The Simpsons.

    But anyway – yeah. So today we’re going to talk about escape velocity and I think the great thing is to kind of go back to – what was it – Newton? Like, who really figured this concept out in the first place?

    Pamela Gay: It was Newton who started to put together the concepts of gravitational potential energy, kinetic energy and the fact that our moon is literally just falling around and around and around the planet Earth. And so Kepler started it all when he realized that orbits aren’t perfect circles, they’re ellipses.

    And then, thanks to the development of calculus, which wasn’t just Newton. We know Leibniz and others were involved as well. They were able to take it from “orbits are ellipses” to “orbits are conic sections”, where you can have parabolas, hyperbolas and then, of course, our beloved ellipse. And each of these different shapes corresponds to a different way that energy’s involved in describing the motion.

    Fraser Cain: And so, what was that big – I mean, we always think about that apple idea about gravity and stuff. What was this, you know, Newton’s watching an apple fall and then he thought, “Oh, I see. Everything’s falling towards the Earth” or that the moon’s the same.

    So what was the – what was this insight that he had and how that led to this concept of escape velocity?

    Pamela Gay: Well, it boils down to three different things coming together at once. First you have the idea that was put forth initially, in part, by Galileo that an object in motion tends to stay in motion. It was Galileo that worked to figure out friction and figure out how inclined planes worked and gravitational potential energy becoming kinetic energy. Those words weren’t fully developed with Galileo. It took a while to develop everything out.

    And then you had Newton coming up with the idea that force is a way of describing mass times acceleration. So now you have forces acting on objects in order to accelerate them. So you have an object, the moon, that is travelling with a velocity that would like to be a straight line. So, since the moon isn’t traveling in a straight line; since it does continue to go in circles around our planet, which is going in circles around the sun – so really, the moon’s spiraling – That means there must be a force acting on it and, in this case, the force of gravity.

    And, well, if it’s falling but going in a straight line, how is it that it’s not hitting the Earth? And it’s that combination of, well, it’s moving along the orbit and falling and the rate of falling is such that it just misses the surface over and over and over again.

    Fraser Cain: Right. And he had this analogy that if you, like, shot a bullet or from a cannon –

    Pamela Gay: Cannonball.

    Fraser Cain: A cannonball. Yeah. Yeah. So, how did that work out?

    Pamela Gay: Well, the idea is that if you throw a ball or very weakly fire a cannonball, it’s going to try and move forward with set velocity but it’s going to end up curving down to the surface of the planet, Earth.

    And, if you’re working on calculating these equations for small enough regionally – you can assume the Earth is flat for the region and the calculation – you can use constant forward velocity to figure out how far it goes across the surface of the planet and then use the acceleration of gravity to figure out how long it takes it to fall from whatever the height of the cannon is above the ground. Work those two equations out and you can figure out where your cannonball’s going to land.

    Well, if you fired the cannonball harder, it’s going to move faster before it finally hits the ground. If you fire it fast enough, the Earth’s surface starts to curve away. So now you have to figure out: Well, there are surfaces curving away. Now where’s it going to end up?

    You work the equations hard enough and you figure out if you fire that cannonball with enough velocity, enough initial velocity, it’s going to sail all the way around the planet and hit the cannon in the butt. And, if you fire it even harder, it’s actually going to fly away from the Earth altogether.

    Fraser Cain: And that “little bit farther” is that escape velocity.

    Pamela Gay: Exactly.

    Fraser Cain: Right.

    Pamela Gay: And, at a certain level, it all comes down to – well, the Earth is trying its gravitational best to pull that cannon down to its surface but, if the kinetic energy is great enough – the kinetic energy, the motion of the cannonball, can act such that it overcomes the gravitational potential energy trying to pull it down.

    Fraser Cain: Well, and so I think you’ve described it as this idea of this cannonball being shot sideways around the Earth and the ball goes all the way around and comes back and –

    Pamela Gay: Yes.

    Fraser Cain: – and hits the cannon or just misses – grazes the top of the cannon, just keeps going, obviously, air resistance is going to pull it in and so on and so forth.

    But what if you took your cannon and you shot it just straight up?

    Pamela Gay; In this case, on small scales, it goes up and it comes back down and hits the launch pad. If you launch it a little bit further, well, the rotation of the Earth at the surface is going to be such that the two are sort of moving together. You add in air resistance and things, it doesn’t end up landing directly on the launch pad anymore.

    Fraser Cain: Well, let’s imagine that it does. I mean, just, you know, in a – sort of, your cannon’s on a vacuum and the planet’s not rotating. I mean, you know, we’ve talked about the idea of you shooting into this circular orbit but I guess, if you shot it straight up, how hard would you have to be able to shoot the cannonball? Like, is it possible that it would – you could make it never come back or will it always come back?

    Pamela Gay: Yes, yes. In fact, you just have to fling it at 11.2 kilometers per second and this is the velocity at the surface of the Earth, assuming sea level and all that sort of stuff, at which the kinetic energy, the ½ m v-squared energy of the rocket at launch, is able to overcome the gravitational potential energy at the surface of the planet.

    Now, if you launch from higher up, you can go slower and this actually means that you don’t have to maintain that huge velocity the entire time you’re trying to escape.

    Fraser Cain: But isn’t the – like, the Earth. I mean, the gravitational field of the Earth extends pretty much across the entire universe, right?

    Pamela Gay: Right.

    Fraser Cain: Just very, very small amounts as the further away you get. So, it’s always going to be pulling on the cannonball, it’s just that it won’t be pulling on the cannonball hard enough to pull it back in.

    Pamela Gay: Exactly. And the truth is that, if you have zero velocity and you’re set down in the gravitational field of our solar system – so let’s say zero velocity relative to the sun. You need something to be relative to if you’re measuring velocity.

    So, if you used the sun as .00 – in our new coordinate system, 000. It’s three-dimensional – and you have no velocity relative to the sun, as a planet sweeps by, its gravity is going to give you motion. So will the sun. And eventually, you’re going to end up falling into something.

    It’s only when you have some sort of a kinetic energy that you’re able to escape all of these different gravitational pulls.

    Fraser Cain: Right. And so, what has an effect on the – again, assuming this planet in a vacuum – what has an effect on the escape velocity? You mentioned – was it 11.2 –

    Pamela Gay: Kilometers per second.

    Fraser Cain: Kilometers per second. That’s really fast. Right? I don’t think people realize just how fast you have to be going to get off the planet.

    Pamela Gay: Well, it could be much worse. So our sun, for instance – I’m looking at a table here – Our sun has 617.5 kilometers per second. So, I – I’m not sure I’ve gone 600 kilometers per hour, except in airplanes. And you have to be going the rate that an airplane, going fairly fast, goes in one hour except you have to go that distance per second to get off the surface of the sun.

    Fraser Cain: Wow.

    Pamela Gay: Yeah.

    Fraser Cain: Right. And so what has an effect? I mean, obviously, like, the mass is –

    Pamela Gay: Right.

    Fraser Cain: – is the big part.

    Pamela Gay: But that’s only half of it. And it’s actually not the bigger half of it because your distance from the center of the mass is actually a factor that gets squared. So, when you look at the force of gravity on the surface – the surface gravity that you’re being subjected to – that surface gravity is the gravitational constant, which is what puts metric into the universe’s units, times the mass of yourself, times the mass of the object you’re on, over the radius between you and the center squared. So that’s the force that you’re experiencing.

    Now the potential energy, it luckily doesn’t have that radius-squared anymore but it’s still there. In this case, the gravitational potential energy is the force multiplied by your distance. So you have: GMM; so your mass, Earth’s mass, gravitational constant, all over a single distance between you and the center of mass. So, if we made the Earth significantly smaller, the gravitational potential energy that we’d have to escape from at the surface would get much bigger. So, if we kept the same mass of the Earth and we cut the radius in half, the potential energy would double.

    You with me?

    Fraser Cain: I am, yep.

    Pamela Gay: Okay. So then, our kinetic energy – that’s the energy of motion. So, when I jump up, at the moment my feel leave the ground, I have a velocity. Now, that velocity decreases the higher up I get until it hits zero and I reverse direction and go back down towards the surface of the Earth.

    The way that my velocity varies is this combination of kinetic energy going down, maximizing gravitational potential energy; gravitational potential energy going down as kinetic energy goes back up as I get closer to the surface, as I fall.

    Fraser Cain: Right.

    Pamela Gay: So that kinetic energy is one?half because one?half is – its reasons take university physics.

    Fraser Cain: Yeah, reasons. My favorite explanation, “because reasons.”

    Pamela Gay: And times the mass, times the velocity squared. So, there’s a mass on both sides of these equations. So the reality is my mass has nothing to do with the escape velocity. I can cancel that out on both sides. So what I’m left with is velocity squared is proportional to the mass of the object over the radius of the object, when it comes to trying to get off of a planet. And the faster you go, the easier it is to escape.

    Fraser Cain: And so how much – so the – If you cut the radius of the planet in half, essentially make it twice as dense – four times as dense? I’m just trying to think how much more dense that makes it. Then, what impact does it have on the escape velocity? Is it double or does it go up by the square?

    Pamela Gay: No. It’s a square issue. So it’s velocity squared. So now, it’s the square root. So, it would be – you’d have to go the square root of 2 faster.

    Fraser Cain: Right. I see. Okay. Yeah, so that has – As you said, that is –

    Pamela Gay: This is so much easier to teach with a chalkboard, I just have to say.

    Fraser Cain: With a chalkboard. I know. I know those times – and, you know, with the video, we should let you bring out the whiteboard and actually start doing the math. But, no, no, no – this is a good – this is a good experiment.

    Right, okay. So then, let’s take a look at some other objects in the solar system. You talked about the sun.

    Pamela Gay: Right.

    Fraser Cain: You’ve got a handy table in front of you.

    Pamela Gay: I do.

    Fraser Cain: So what are some other objects that, you know – What’s the escape velocity from some other objects in the solar system?

    Pamela Gay: So Ganymede, a happy little moon, it’s 2.7 kilometers per second; Pluto is just 1.2 kilometers per second, so that’s not that bad in the grand scheme of things; Mercury, 4.3; the Moon is just 2.4 kilometers per second, so it’s actually fairly easy to get things off the moon in the grand scheme of things. Jupiter’s a bear. Jupiter’s 59.5 kilometers per second.

    Fraser Cain: Right.

    Pamela Gay: And so, it’s tricky. Now, one of my favorite things is the gravitational acceleration at the surface of Saturn is very similar to what it is at the surface of the planet, Earth. But, because the gravitational acceleration that you deal with is proportional to the radius squared, the potential energy you need to escape isn’t the same on the two objects. So, on Saturn, you have to go a whole lot faster. You have to go 35.6 kilometers per second to escape, unlike Earth’s 11.2.

    Fraser Cain: So let’s imagine some futuristic rocket ship that is going to travel outside of the Milky Way, for example.

    Pamela Gay: Okay.

    Fraser Cain: So we’re gonna need to, first, escape from the Earth.

    Pamela Gay: Right.

    Fraser Cain: So we’re gonna need to go that 11.2 kilometers per second to get off the Earth.

    Pamela Gay: Yes.

    Fraser Cain: Then we’re gonna need to escape the sun.

    Pamela Gay: Yes, so –

    Fraser Cain: Not from the surface but from far away.

    Pamela Gay: Right, right. So that one isn’t too big a deal. I don’t have that number in front of me, of course.

    Fraser Cain: No, no. But – you know what? I highly recommend – I know you – I don’t know if you’ve played it yet but I highly recommend the Kerbal Space Program.

    Pamela Gay: Yeah, yeah. No, I know Kerbal is awesome.

    Fraser Cain: Yeah. This stuff all now utterly makes sense to me and – right? Because I’m like, you know – I know how big to rocket I gotta build to be able to make it be on a solar escape velocity.

    Pamela Gay: Right. So I just don’t know what the sun’s escape velocity is at, like, the distance of Voyager. I know, from the table I’m looking at, that, at the distance of Neptune, you have to be going 7.7 kilometers per second to escape the galaxy – not galaxy, the solar system.

    Fraser Cain: Right.

    Pamela Gay: And then, to escape the galaxy from our solar system’s distance, it’s, well, more than 525 kilometers per second. And I’m being guilty of using Wikipedia for all of these numbers for people who want a citation.

    Fraser Cain: Right.

    Pamela Gay: So, you have to get going pretty darn fast if you want to escape our galaxy. So you’re looking at, that’s the number that you care about most is the biggest number. So, you need to be going greater than 525 kilometers per second to escape our solar system.

    Fraser Cain: And the amazing thing is, is that we’ve talked about this in the past, that there are stars which are on this escape velocity –

    Pamela Gay: Exactly.

    Fraser Cain: – that have gone through interactions or gotten exploded by supernovae or something and they’re outta here.

    Pamela Gay: They got a good kick. They were given a kinetic energy that can overcome that gravitational potential energy.

    Fraser Cain: As always, I like to go to extremes. So I’d like to go – First, I’d like to go for the, like, really low escape velocity.

    Pamela Gay: Okay.

    Fraser Cain: So what are some places in the solar system where it’s very low and what could you do?

    Pamela Gay: Well, some of the asteroids are just barely able to hold on to even smaller asteroids. And so, in these cases, you have these very gently arching small moons around building- – giant building, admittedly – sized asteroids. So that’s not a whole lot of gravitational potential energy but they’re still able to hold on to these things. And if an asteroid gets small enough, then, were you able to very carefully get yourself on to the top, you could spring yourself off and fly away. And that’s just kind of cool to think about asteroid-hopping – literally, asteroid-hopping –

    Fraser Cain: Yeah, literally.

    Pamela Gay: – because the asteroids are very far apart. So –

    Fraser Cain: Right.

    Pamela Gay: You can’t really bounce from one to another. Or you could see one from another.

    Fraser Cain: Right. But the bottom line is, is that if you’re not careful and you’re some asteroid miner on the wrong-sized asteroid with a low enough density, you could very well jump and just not come back.

    Pamela Gay: Here I think we’re talking about asteroids that are so small that mining them’s kind of a pointless endeavor. So, we’re good.

    Fraser Cain: Right – Dismantling them because they’re just a little rubble pile.

    Pamela Gay: Right, right.

    Fraser Cain: Yeah. Yeah. But that’s kind of scary, right? It makes me think of Gravity, you know, the movie.

    Pamela Gay: Which I still have not seen.

    Fraser Cain: Ooh. Go see it.

    Pamela Gay: I was out of the country.

    Fraser Cain: I know, I know, I know and they don’t have that movie in that other country. Anyway, so – right. So that’s really light. I mean, you can imagine these situations and there’s these – you know, I’ve seen some of the mission plans for some of these asteroids. It is essentially that you are weightless. I mean, you’re not walking across the surface –

    Pamela Gay: Yeah.

    Fraser Cain: You are – you know –

    Pamela Gay: Trying not to fly off of the surface.

    Fraser Cain: Yeah, you’re bolting on a ladder-type system that you’re gonna crawl around the outside of this asteroid on and bolt yourself in, like a rock climber, to try and stay connected.

    Pamela Gay: Right.

    Fraser Cain: Okay. Well then, let’s go the other way. So, let’s go to extremes. Like, what about white dwarfs?

    Pamela Gay: So white dwarfs are kind of obscenely dense. A tablespoon of them is more than several elephants’ worth of mass. And to escape one of these, you’re looking at having to go roughly 4.5 million kilometers per hour. So, it’s a lot.

    Fraser Cain: Thousands of kilometers per second. Yeah.

    Pamela Gay: Yeah, exactly. Not the speed of light but –

    Fraser Cain: No.

    Pamela Gay: Really darn fast.

    Fraser Cain: No. But we’ve talked about, in another show, an even more exotic object, which is a neutron star, right? This is the situation where the gravity has pulled the electrons and the protons together and all you got is neutrons.

    Pamela Gay: And here you’re just adding a couple of zeroes. So this is now a hundred times faster, so you’re looking at 450 million kilometers per hour.

    Fraser Cain: I just worked on an article about this. It’s 100,000 kilometers per second. So it’s a third of the speed of light?

    Pamela Gay: Yeah. So, these are objects so dense that even protons and electrons can’t stay apart.

    Fraser Cain: Right. And only light can escape from them.

    Pamela Gay: Yes.

    Fraser Cain: And it does. I mean, you get pulsars. So you got a situation where light is escaping from them. So now, the final solution here for the most extreme, densest object, highest escape velocity, is a black hole, right?

    Pamela Gay: Yes. And a black hole, by definition, the lowest possible escape velocity is the speed of light. And we don’t quite know where the surface of a black hole is. So we generally define them as having an escape horizon. And the escape horizon is that point at which you’re so far away from the black hole that – and so near, at the same time – So it’s this balancing point where, if you got any closer, you’d have to go faster than the speed of light to escape. But if you went any further away, you could escape going slightly under the speed of light. But at that Schwarzschild radius, you have to go the speed of light, which you can’t. So you can’t escape.

    Fraser Cain: Right. And I guess the size of that Schwarzschild radius, that event horizon, changes depending on the mass of the black hole. You got –

    Pamela Gay: Exactly.

    Fraser Cain: – the super-massive black hole and it’s the size of a solar system.

    Pamela Gay: Right. And you get a microscopic black hole and it can slide down between molecules.

    Fraser Cain: Wow. Yeah, it’s a funny thing about black holes that really, it’s all just about compressing the mass down.

    Pamela Gay: Exactly.

    Fraser Cain: You could have –

    Pamela Gay: How close to that center of mass can you get?

    Fraser Cain: Can you get – and then it turns into a black hole.

    Pamela Gay: Right. So you can have extraordinarily small black holes that don’t even have all that much mass but the amount of mass they have is in such a tiny, tiny, tiny space that you could get close enough to the surface that you’d need to go the speed of light to get away.

    Fraser Cain: And so then, I mean, we don’t know what’s inside of a black hole, right?

    Pamela Gay: No, no.

    Fraser Cain: So we don’t know if there is a place inside that is infinitely small. Like, who knows what the actual escape velocity of a black hole might be.

    Pamela Gay: Well, we don’t know if they have a surface.

    Fraser Cain: Right.

    Pamela Gay: So that starts to make the question silly. If they do have a surface, it’s quite feasible that the escape velocity can be thousands of times the speed of light for some of these objects – perhaps even more. We don’t know how small things compress down. We don’t know what state of matter they achieve. There’s a lot we don’t know.

    And so, just as Newton came along and took Kepler’s ideas and made them science; Einstein came along and modified Newton’s ideas to work under relativistic extremes and now we need that next person who comes along and grows the theory so that we start to understand what’s happening within the escape horizon.

    Fraser Cain: Could a black hole get smaller than the Planck length?

    Pamela Gay: We don’t know.

    Fraser Cain: Don’t know. So imagine, like, a super-massive black hole; like the most massive, super-massive black hole in the universe – that much mass but the size of a Planck length, what would the escape velocity be? Someone do the math.

    Pamela Gay: I’m not going to calculate that.

    Fraser Cain: Someone do the math! That would be a horrible number. Yeah, yeah, that would be amazing. Cool.

    Well, thank you very much, Pamela.

    Pamela Gay: It’s my pleasure. Thank you.

    Male Speaker: Thanks for listening to Astronomy Cast, a non-profit resource provided by Astrosphere New Media Association, Fraser Cain and Dr. Pamela Gay. You can find show notes and transcripts for every episode at astronomycast.com. You can email us at info@astronomycast.com. Tweet us @astronomycast. Like us on Facebook or circle us on Google Plus.

    We record our show live on Google Plus every Monday at 12:00 p.m. Pacific, 3:00 p.m. Eastern or 2000 GMT. If you missed the live event, you can always catch up over at cosmoquest.org. If you enjoy Astronomy Cast, why not give us a donation? It helps us pay for bandwidth, transcripts, and show notes. Just click the donate link on the website. All donations are tax deductible for US residents.

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    Duration: 28 minutes

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    5 Responses to Ep. 318: Escape Velocity

    1. Robert November 1, 2013 at 3:16 am #

      I always imagined that the solar wind existed in part by virtue of the lightness of its particles, but your show suggests that the weight of the object that needs to attain escape velocity is not a factor, which means that the Sun expels these protons etc. at enormous speeds. Just how fast do they travel, and how much faster is this than the Sun’s minimal escape velocity? The subatomic particles that compose the solar wind are regularly described as “high energy.” How does their speed correlate with this energy?

    2. Richard Hubbard November 2, 2013 at 11:42 am #

      In case anyone is not quite “seeing” the cannon analogy, there is a great little website called “Newton’s Cannon” that illustrates the idea…

      http://waowen.screaming.net/revision/force&motion/ncananim.htm

      // why yes, I am a teacher, why do you ask? 🙂

      • Robert Madewell December 30, 2013 at 8:14 am #

        4411 is the lowest number that will orbit the earth and hit the canon in the butt.

    3. Tech November 2, 2013 at 3:42 pm #

      I cannot hear clearly, it runs and stops and runs… What’s wrong?

    4. Mark November 26, 2013 at 6:38 pm #

      You don’t have to be going at the escape velocity to get away from an object unless you’re coasting. If you have something pushing you (such as a rocket engine) with enough force, you can even escape from inside a black hole’s event horizon. Keep pushing long enough and you’ll reach a point where a modest velocity will allow you to escape from the black hole without further pushing.

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