Date: December 26, 2011

Title: The Great Escape (Velocity that is)

Podcaster: Julia

Description: So, just what in the Solar System can you actually jump off?

Bio: Proud owner of a VMT (Very Medium Telescope) with an interest in all things Astronomical. I live in Adelaide, South Australia where if there’s anything interesting to look at in the sky, you can guarantee it will be cloudy. I’ve contributed readings to Steve Nerlich’s CheapAstro podcasts (www.cheapastro.com) and thought I’d give it a bit of a whirl myself.

Sponsors: This episode of “365 Days of Astronomy” is brought to you by Cosmic Vibrations. Bringing you experimental ambient music featuring sounds from the cosmos. Visit www.reverbnation.com/kiddscosmicvibrations.

Transcript:

Hi, my name is Julia and this is my contribution to the 365 days of astronomy podcast.

One thing that I’ve always been curious about is how small an object in space would need to be so that you could literally “jump” off it and careen off into space never to return.

Going by a quick internet search, I’m not the only one – so I thought I would have a look for the answer and share this with you all.

Surprisingly and disappointingly, there isn’t any sort of handy dandy list out there. I did find plenty of other curious people asking the same question but in looking for a quick answer I found two obstacles:

1. The majority of people answering the question went into a wonderful frenzy of page after page of complicated equations, which was all very impressive, but didn’t really help the person who just simply wanted to know how high they could jump on the Moon.
2. The person asking used a height they (apparently) could jump on Earth as being, well certainly beyond any height I could jump without a pole vault, a trampoline or rocket-propelled pogo stick.

So I decided to have a bit of a bash at figuring it out myself.

And here I need to give a disclaimer : I have no formal education in physics, and other than being reasonably smart (I can tie my own shoelaces) I am essentially a layperson.

I figured the first bit of information I needed to gather, is just how high you can jump on Earth. And I’m talking about an average person, of average height and weight (which I happen to be) and not a high-jumper, basketball player or pole-vaulter.

Several jumps against a measuring stick later: For the record I did a straight “jump up” – standing start, bent knees and then pulling my feet up. I cleared the measuring stick at around 50cm (or 20 inches for those who entered the 21st Century kicking and screaming). I’m sure there are some tall, springy athletic folk out there who can top that, but I’m trying to get a vibe for the average person, so I’m sticking to the 50cm figure.

With this figure I then needed to calculate the jumping velocity. And here’s where I broke my brain. In fact I broke it so much I actually went off on a tangent calculating jumping heights by gravity percentages and got myself all scrambled up. I was thinking I needed to find out how high I could jump on various objects. As it turns out that was a mistake, I didn’t need to calculate that at all, plus I incorrectly used the ‘how high’ figures to get jumping velocity and well, it took the wonderfully helpful Steve Nerlich and “the guys” to (warning: bad pun coming up) bring me back down to Earth.

All I really needed to do was calculate my jumping velocity, and then compare it to the object’s escape velocity and voila! But I’m leaping (ha ha!) a little ahead here.

Anyhoo – to calculate jumping velocity, well I have to give a big shout out to Steve and “the guys”, they fixed up my equation so that I had a lovely formula that started with a Square Root, and had my Jump Height in there with the Surface Gravity and all sort of brackets, minus and multiply signs that don’t really translate to a podcast.

Ah, but one of the components of that formula is “Surface Gravity”, so um, how to you figure that out?
Well, remember how I mentioned those very clever folk who responded to forum questions with lengthy equations? As it turns out, those nasty equations with Rs and Ms and various other squiggly things that only vaguely resemble letters were exactly what I needed. One quick lesson on Newton’s Gravitational Constant later and how to plug powers into Excel and I had a nifty keno formula which is again way too long to spell out here.

In order to work out the Surface Gravity, I needed the radius and mass of the object. So, off I went to gather the radius and mass of everything I could find well, the radius and mass for. After consulting the Intertoobes on websites with confidence boosting URLs containing acronyms like “N-A-S-A” and of course the old standby of Wikipedia, I ended up with a rather nice spreadsheet of a fair chunk of the objects in the Solar System in Radius order from largest to smallest.

Let’s start with Earth. Radius, 6,371 km and a mass of 5.9736 x 1024 and once I plug those figures into the aforementioned too long formula I get a surface gravity of 9.81. Hmmm, where have I seen that figure before? I came across this figure a number of times when trying to look up how to do this. And I’m sure for those who’ve studied physics you’re all going “oh duh” at me, but remember I’m a layperson here. Well for those of you like me, that figure is referred to as ‘standard gravity’ or if you want to be technical, the acceleration Earth imparts to objects on its surface. In a nutshell, Earth’s Gravity. Hey! I guess I’ve got this right then.

So, with a jump height of 50cm, and the Earth’s Gravity of 9.81, that gives me a Jump Velocity of 3.13 metres per second per second. Which (and you’ll thank me for this later) I will from now on refer to as “mss”. Oh, and this, by the way is a constant, unless I go on a diet or eat too much chocolate my mass will be the same no matter where I am. I might weigh a sixth less on the Moon due to the force of gravity being less, but my mass doesn’t actually change. Since Surface Gravity is part of the equation my jump velocity will always the same no matter where I’m jumping from.

Another disclaimer:
I refuse to get bogged down in factoring a spacesuit and associated breathing apparatus etc, since it won’t make any real difference. So in my little pretend Universe I have lucked into finding an alien device that protects me from all those nasty things like vacuum, heat, cold, radiation etc – and therefore I have no added spacesuit mass to deal with. And while I’m doing disclaimers: I do know about the “square of the distance” thing – again, keeping it really simple.

Escape Velocity: More maths – more pain for the brain.

Fortunately the larger objects have their Escape Velocity figures in both Wiki and on a NASA site, and even a fair number of the smaller ones. For those I didn’t have figures for, the equation for Escape Velocity is easy to find (more Square Roots of Gs, Ms and Rs). So I just needed the surface gravity (which I have calculated already) and the mass and radius (oh look I have a list of those) and off I went.

Unfortunately we don’t have the mass of a lot of the smaller objects, and mass is VERY important as it turns out. Here’s an example why:

Comparing the planets:

Mercury – Radius 2,440km – Surface Gravity 3.7 mss which is 38% of Earths
Venus – Radius 6,052km – Surface Gravity 8.87 mss which is 90% of Earths
Mars – Radius 3,390km – Surface Gravity 3.7 mss which is 38% of Earths

Hang on, Mercury’s radius is smaller than Mars by 1,000 km but yet, it has the same gravity – being (how can I put this delicately) a little on the heavy side. It’s definitely mass and not size that’s really key here, and so I really do need the mass to figure these things out, darn!

So onwards I go with my calculations – Moons and Asteroids and Comets – oh my!

Armed with my pile of lovely equations and their results, off I went to find something I can jump off with my jump velocity of 3.13 mss.

Earth – Escape Velocity 11.2 KILOmetres per second per second or 11,200 mss – Jump Velocity 3.13 mss. That’s a negative, but then we knew that already – otherwise we would have gone to the Moon a LOT sooner than we did.

And we can pretty much rule out all the other planets – even little itty bitty ex-planet Pluto where you need to jump at 1,200 mss before you’re officially designated another Plutoid.

So, how about moons? Our Moon, we’ll we know for sure that we can’t jump off it though a few of the Apollo Astronauts gave it a good try. Apollo 16 Astronaut John Young seems to be a bit of a serial jumper and there are a lot of great photos and videos of him doing just that. Even so, he still didn’t manage to launch himself into orbit.

The same goes for the other big roundy moons, like Jupiter’s four Galilean Moons and Saturns bigger moons like Titan, Enceladus, Mimas & Iapatus.

But what about the smaller more “potatoey” moons? Maybe, here we might have more luck.

Mars has two small Potato-shaped Moons, how about those?

Phobos has a radius of 11km and a mass that gives it an escape velocity of 11 mss. So, no, you can’t jump off Phobos. You would need that Pole Vault. Though with its close proximity to Mars (and it’ll get even closer and either break up or crash one day) you wouldn’t really want to as you’ll probably end up being captured by Mars and well – splat!

What about Deimos? Well, it has a VERY soft surface, so getting a jump going might be a bit like trying to leap out of a vat of talcum powder, but let’s say you find a nice hard rock to stand on. With a radius of just 6.2km it has an escape velocity of . . . wait for it . . . 5.6 mss. Sorry, no. You would be able to jump pretty high though – and I do mean high. Almost 2 km straight up – but you’d still come back down, just very, very slowly – so you might want to pack a lunch . . . and maybe a dinner.

What about Asteroids? Just how many of these puppies can we launch from?

Well, the biggest one is Ceres, and it’s Escape Velocity is 517 mss – so that’s a definite no.

Same goes for the next biggest Asteroid, Vesta and a fair chunk of the others, well basically anything over around the 5km radius mark.

But once you do get down below that magic 5km radius, as long as the mass is also low, off you go. These include Remus (which is actually the Moon of an Asteroid) and you might be familiar with Itokawa (of the Japanese Hayabusa return sample mission fame) and also the potentially scary Apothis, which , if it does crash into Earth in a few decades, at least you now know that any rugged oil drillers sent there to destroy it before it hits will have to take care not to jump around too much.

And of course there’s a bunch of smaller stuff out there with very unimaginative titles like (144898) 2004 VD17 which you’ll have an awful hard time holding on to.

So how about further out into the Solar System?

Jupiter has an awful lot of tiny moons, most of which are probably captured asteroids, so it wouldn’t be much of a surprise to find that you can have a bit of a bounce around the Jovian system. Unfortunately we don’t have mass figures for a lot of these (not that I’m complaining, as most of their names are horribly unpronounceable), but I can at least tell you that Carpo, Kale and Euporie are worth a shot.

Saturn also has many small moons, most of which we had no idea existed until Cassini plonked itself into orbit. Even so, we don’t know the mass of most of them, but at least I can tell you that you can have yourself a bit of fun jumping off Daphnis, Pallene, Polydeuces & Methone.

For Uranus it’s a no go for it’s bigger Moons like Titania, Oberon and Miranda, even down to Cupid with a radius of 9km – the only potential I could find is Mab with a radius of just 5km, but without it’s mass I can’t say for sure.

Neptune is a bit of a party pooper – most of its moons are just too big. But then again, we’ve only done a quick flyby of both these worlds and without something handy like Cassini orbiting them we really don’t know if they have a plethora of tiny little moons we just don’t know about.

Same goes for Pluto’s band of Kuiper Belt Object buddies. If we can detect them – they kinda have to be fairly big (and shiny), so the ones we KNOW of, sorry – not jumpoffable.

But, what about comets? There’s only a few we have data on and they have very familiar names. You might know of Comets Halley, Tempel and Hartley – and yes you can jump off them. If you can catch them that is.

So there you go. Tiny Moons, Asteroids and Comets that have a radius of less than 5km and not too “massy” are small enough for the average person without too bulky a spacesuit to jump off.

Anything bigger and you would need to order that Rocket Propelled Pogo Stick from ACME.

End of podcast:

365 Days of Astronomy
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