| MadSci Network: Astronomy |
The force of gravity between two bodies is given by a simple formula that Isaac Newton came up with over two hundred years ago. In mathematical form it says that:
F = (GMm)/r2
Where M and m are the masses of the two bodies and
r2 is the square of the
distance between them. G is a quantity known as the universal
gravitational constant. In words, Newton
might have said "the force of gravity between two bodies is directly
proportional to their masses and inversely proportional to the square of
the distance between them.
It's a common misconception that the weight of a person is given in kilograms. Kilograms is a measure of mass. Weight can be measured in pounds or in Newtons (yes, named after that very same guy).
We know the mass of the Earth and the size of the Earth, so we can
calculate the strength of the Earth's gravitational field at the surface.
This is represented by g.
g = GM/r2
The weight of a person on the surface is equal to the force of gravity on that person.
W = F = mg (3)If you compare this formula to the first one, you'll see that they're the same.
That's how we measure the weight of a person on the Earth. Now the strength
of the gravitational field is different for different planets, but we can
easily calculate g for another planet if we know its mass and
radius.
For Earth g = GM(earth)/r2(earth) = 9.81 m/s2
For Mars g = GM(Mars)/r2(Mars) = 3.73 m/s2
Astronomers have studied the planets in our solar system and derived their masses by watching how their moons (and spacecraft that we send) move. We also know the planets' radii by measuring their angular diameters and knowing how far away they are. So we can calculate the gravitational field strength at the surface of any planet.
Once we know g, it's easy to calculate the weight. Just use
equation 3.
On Mars, you would weigh about 40% as much as you weighed on Earth. So you never need to diet. Just travel to other planets :-)
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