How much would I weigh?
Published on Nov 30, 2006 at 7:50 pm.
12 Comments.
Filed under amusement, physics.
When the Apollo astronauts walked on the Moon they wore spacesuits to protect themselves from the vacuum of space, and they had to carry all of their air and life support equipment with them. These spacesuits weighed about 180 pounds here on Earth, but when you look at the astronauts on the Moon, they are bouncing around as if they don’t even notice the weight of their suits. This is because the Moon’s gravity is much less than Earth’s, so the astronauts and their spacesuits togehter weighed about 50 pounds or less! So, this begs the question, how much would I weigh on another world?
Yeah, you can look up some things like this, but I wanted to compute it for myself, and while I’m at it perhaps come up with a useful formula for others to find out how much they might weigh on another world. This turns out to be really quite easy. Again, as with my last post, the calculations are something from first semester physics. In that class we see that an equation for the acceleration due to gravity can be easily shown to be
where G is the Universal Gravitational Constant that I introduced in yesterday’s post, M is the mass of the planet (or moon), and R is its radius. To find your weight, then all you need to do is multiply this value by your mass in kilograms. You’ll get your weight in Newtons. Well, that is fine for my physics students. But, an awful lot of my readers are not physics students, and they live in the United States, where we still use archaic units rather than SI units. Most of these people have no idea what their mass is in kilograms. But, they do know their weight in pounds. Even in other countries, people sometimes think of their weight in other units, such as stones. So, perhaps it would be easier to come up with a formula to easily compute your weight in whatever units you like to use. So, I came up with
where W is your weight on the other world, W⊕ is your weight here on Earth, in whatever units you like, and X is a comparison factor that can be calculated using the equation
where M is the mass of the world, M⊕ is the mass of the Earth, D⊕ is the diameter of Earth, and D is the diameter of the world. So, rather than making you figure out these vaules for a bunch of different worlds, I put together a table that shows the X factor for various worlds, and what I would weigh on them. I am appending that to the end of this post.
You can notice a few interesting things, though. Venus is a world that is almost the same size and mass as Earth, so if you go to Venus, you’d weigh just a little less than on Earth. Of course, the pressure and temperature of the Venusian atmosphere would crush and bake you so quickly that you’d never notice. Interestingly, you’d weigh about the same on both Mars and Mercury, even though they are different sizes. That is because Mercury is quite a bit more dense than Mars. I also compared weights on Jupiter’s four biggest moons: Io, Europa, Ganymede, and Callisto. These moons are planet sized bodies. Ganymede is even larger than the planet Mercury (about halfway between Mercury and Mars in diameter), and Callisto and Io are only a bit smaller than Mercury. Each of these moons except for Europa is larger than our Moon, but you’d weigh less on them. That is because they are less dense than our Moon (except for Io). Titan is about the same size as Ganymede, and you’d weigh just a little less on Titan than you would on Ganymede (Titan is also just a shade less dense than Ganymede).
Out of curiosity, I also included Ceres on the list. Ceres is the largest of the asteroids, but even so you’d weigh less than 3% as much on Ceres as you do on Earth. I’d weigh only about 4.3 pounds! Occasionally you read science fiction novels in which the asteroids are colonized. But, under that low of gravity, the human body has all sorts of problems. A few scifi writers go so far as to suggest rotating the asteroid to create a sort of artificial gravity inside (but pointing outward!). The only problem with that, though, is that most asteroids probably aren’t held together very well, so they’d probably tear themselves apart.
I also figured what I’d weigh on Phobos, the larger of the two moons of Mars. Phobos is a tiny little thing. It has so little gravity that I’d only weigh about 1.4 ounces on Phobos!!! In fact, Phobos has so little gravity that its escape velocity (see yesterday’s post) is only about 11 m/s. If you work out the math, that means that if you can throw an object 6.6 meters high on Earth (that’s about 22 feet for my US readers), then if you were to throw it upwards just as hard while on Phobos, you’d toss it clear off of the Moon into orbit around Mars!
-Astroprof
Darnell Clayton on December 2, 2006 at 5:43 pm: 1
Thanks for posting about this!
I was wondering what I would weigh on other lunar worlds.
Quick question. What is the least amount of gravity necessary for a human body to function on a world? Is it one third?
PS
If you made a site that automatically found people’s weight on other worlds (and moons) it would probably become quite useful.
Astroprof on December 2, 2006 at 9:46 pm: 2
I have heard that the human body needs at least 1/3 to 1/5 of Earth’s gravity to avoid the problems that astronauts experience in low gravity environments. However, no one has ever tested that. What we need is to have a rotating space station to simulate low gravity environments and then see how astronauts do with extended stays. Any numbers that you hear are just guesses.
Yeah, when I was making this post, I thought that it might be interesting to have some sort of input that you’d give your weight and it would spit back how much you’d weigh on some other world. But, I didn’t know how to program that, and I didn’t have time to figure it out until perhaps during the break between semesters.
Georg on December 4, 2006 at 5:39 pm: 3
Technically, lb is a unit of mass, not weight, so it is not strictly correct to say “I would weigh 25 lbs on the Moon”, but to be pedantic one would have to say “I would weigh 25 lbf (pounds of force) on the Moon”, where 1 lbf = 1 lb * g (standard acceleration of gravity). I common usage, of course, weight and mass are often confused, and pounds and pounds of force are rarely distinguished; the situation is much clearer in the SI system, where mass is measured in kilograms and force in Newton, making the distinction between mass and weight a lot clearer.
Astroprof on December 4, 2006 at 6:02 pm: 4
Good point, Georg. That\’s why SI units are to be preferred. I almost NEVER see pounds force differentiated from pounds mass. The standard usage is to call both just \”pounds.\” And, most people know their weight by use of a scale, not a balance, so they really are measuring weight, not mass. I SO much prefer the SI system.
sarah is gay on January 3, 2007 at 9:23 am: 5
how much would i weigh if i was 133lbs. thanx gay peps!
Lizzie on March 18, 2007 at 11:45 am: 6
If i weigh six stone on Earth how much would i way on the moon?
Hannah on May 14, 2007 at 2:55 pm: 7
I am doing this extra credit thing for science class and my science teacher wants us to figure out how much i would weigh on one of Jupiter’s moons called Ganymede. I have no clue how to do that thing up there that u showed the web cuz i am not a math kind of person. Could u tell me how much i would weigh if i was 120 pounds on earth and give me the math problem on how to do it? It would help me a whole lot. I got a C minus and i need a better grade.
Thank you so much!
Vincent Sauve on September 3, 2007 at 9:00 pm: 8
Good for you in not listing how much one would weigh on the gas giants. It is extremely common (just check the first 30 or so google hits) for this deceptive weight listing for the gas giants. In order to have a correct measurement of weight one cannot be in freefall or near freefall. These gas giants have no solid surface to put a scale on to measure a weight. (Of course, a persons’ mass is constant.)
What I wonder is where in the depths of the atmosphere of a gas giant would one be likely to encounter the strength of gravity that would be equal to one gravity on Earth. I believe one would not have a weight anywhere near an Earth weight unless they were trying to rocket away from a gas giant.
If we leave aside the question of radiation, temperature, pressure and buoyancy (deep sea animals aren’t bothered by pressure) and therefore use something not so subject to pressure, like a steel ball, at what place in depth would the falling object receive enough friction, i.e. countering force, in its downward travel to equal one Earth gravity? Think of a small scale of the same diameter as the ball below the ball. Hint, if you lightly taped a bathroom scale to your feet and jumped feet first into the Earth’s ocean and ignoring the impact of the surface would you think it likely that you would encounter a density transition zone anywhere near one gravity as you descended?
I think this would be a wonderful and illustrative exercise for physics students.
Students should keep in mind that the mass above counts against the mass below such that at the center of any planet the gravitational effect would be zero.
If someone comes up with an answer for this please send me an email with your answer explained. I would like to see a correct conceptual formulation with as little mathematics as possible for web publication and broad public understanding so as to counter the misleading weights for object near the gas giants.
Vincent Sauvé
skeptica@pacbell.net
http://home.pacbell.net/skeptica
Callum Iz Ere on January 19, 2008 at 3:00 am: 9
if i weighed 5.5 pounds on Earth how much would i weigh on Jupiter?
kyle on May 22, 2008 at 7:46 pm: 10
how much would i weigh on eris if i was 100 pounds?
Titanic Titan on July 27, 2008 at 5:00 pm: 11
What is the formula for anyone’s weight on Phobos, Io, Titan, Sycorax, Proteus, and Charon? All of them are in our solar system.
Please answer this for a project I am doing. If an answer is found, please email me at Galileo1995@gmail.com. Thanks
Titanic Titan on July 27, 2008 at 5:02 pm: 12
p.s, they are moons.