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Repost: Does this planet make me look fat? *July 27, 2010*

*Posted by mareserinitatis in Uncategorized.*

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I’m a bit drained tonight, so I’m punting and moving over a post from the old blog. If you need to brush up on your algebra, this is just the thing.

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When kids are first learning algebra or physics, it’s often fun to start out with activities pertaining to space. Most kids are curious what it’s like on other planets, so being able to determine certain mathematical values may seem less boring than other types of practice exercises.

With that in mind, I have two activities relating to space. The first activity, which I will post below, relates to a person’s weight on each planet. (For a version with no math, take a peek here. You can also use this to check your figures.) This activity will be a bit easier than the second activity, which I will probably post next week. That activity deals with age.

**Does this planet make me look fat?**

Most people have seen videos of astronauts bouncing around in the moon or floating in a ship in space. This doesn’t mean astronauts have suddenly gained super powers but that they weigh less in space or on the moon. However, on other planets, a person may actually weigh more.

We can figure out how much more or less by using Newton’s Law of Gravitation:

(Eq. 1) .

Newton figured out that how much you weigh (F, or the force of attraction between you and a planet) is equal to your mass (m) times the mass of the planet (M) times the gravitational constant (G) divided by the distance between you and the planet (r) squared.

What this means is that the more mass the planet has, the stronger the force or the more you weigh. If the planet has less mass, you will weigh proportionally less. If you double the weight of the planet, the force will also double.

However, the force is inversely proportional to distance (r). If you double the distance, you don’t halve the force; the force decreases by 2^{2} or 4. Your force becomes a fourth of the original value.

The gravitational constant (G) is basically a number that shows the relationship between mass and force. It is the same everywhere in space, so it doesn’t matter what planet we’re on: we can use the same gravitational constant.

The problem with using Newton’s law in the US is that most of us know our weight and not our mass. (In other countries, most people know their mass because they use the metric system.) Fortunately, it’s not an insurmountable problem.

Ex 1. Solve for your mass in kilograms, given the conversion 0.453 kg/lb.

Ex 2. Now you’ll find your mass a second way, using the value in Ex. 1 as a check. Find your weight (or force) in Newtons, given the conversion 4.448 Newtons/lb.

Ex 3. Take Eq. 1, leaving it in symbols, and solve for m.

Ex 4. Now that you have an equation for your mass, solve this equation using your value for Ex 2 as your force, 6 370 km as your radius (which is the radius of the earth…but you’ll need to change this to meters…as you will for future exercises), 5.975*10^{24} kg as M (this is the mass of Earth), and 6.672*10^{-11} N m^{2}/kg^{2} as the gravitational constant.

Ex 5. Compare your answers for Ex 1 and Ex 4. Specifically, find your percent error:

What this tells us is that our weight is actually the force of attraction between our body and Earth at Earth’s surface. As we move away from Earth, our weight will change (but not our mass!). If we are on the Moon, our weight will be the attraction between our body and the Moon. Therefore, we can use this formula to determine our weight pretty much anywhere.

Ex 6. Let’s start by imagining we’re on the space shuttle. The space shuttle sits in Low Earth Orbit (LEO) at around 330 km above the surface of Earth. Find your weight on the space shuttle. Solve Eq. 1 for F.

Ex 7. Now we want to determine our weight on the surface of the Moon. The Moon has a mass of 7.343 *10^{22} kg and a radius of 1 738 km.

Ex 8. Now check out your weight on Jupiter. Jupiter’s mass is 1.8986*10^{27} kg and has a radius of 142 984 km.

For information on the other planets, please check out The ~~Nine~~ 8 Planets.

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