Hey smart people, Joe here.
What weighs more?
A pound of feathers, or a pound of steel?
Ah, sorry, I forgot to switch the video into metric.
Much better.
So what weighs more, a kilogram of feathers or a kilogram of steel?
You’re too smart.
You’re right, that’s a trick question.
A kilogram of feathers and a kilogram of steel… it all depends on where on Earth you weigh
them.
[OPEN]
Something’s mass–a kilogram of feathers, a kilogram of steel, or you and me–is constant
everywhere in the universe, because mass is a measure of how much stuff there is, all
your atoms added together.
But weight isn’t a constant.
It’s the force gravity applies to all that stuff at one specific spot, so depending on
the gravity where you are, your weight will be different.
This makes sense if we think about being, say, on the moon, where your moon weight is
about sixteen and a half percent your Earth weight, because gravity is about sixteen and
a half percent of what it is on Earth.
But the same thing is also true here.
Things don’t weigh the same everywhere on Earth.
So, a question: Where on Earth would you, or feathers, or steel, weigh the most?
And for that matter, where would you weigh the least?
What makes this question so confusing is there’s more than one definition of “weight”.
To most of us, weight’s just the number you see when you step on the scale.
A scale does measure weight, the force gravity puts on a mass, but the numbers on the scale,
in kilograms or pounds, are not measures of weight.
Officially, those are measures of mass, and like we just saw, mass and weight are different
things.
So unless your bathroom scale gives you an answer in Newtons, it’s lying to you.
Now, mass is the amount of stuff there is in you, and weight is how hard gravity is
pulling on you and all your atoms.
Most of the time this difference doesn’t matter, because if you weigh two things in
the same place on the same scale, they’re both under the same influence of gravity.
But a kilogram of feathers on the north pole, weighs more than a kilogram of steel on the
equator, and the reasons why are pretty weird.
All this would be easy to figure out if the Earth were a perfectly smooth non-rotating
sphere floating alone in space, nice and uniform all the way through.
On a planet like that, gravity would be the same everywhere on its surface.
But we don’t live on that spherical planet.
First problem is, the Earth is spinning.
Well, actually that’s not a problem.
It’s kind of a good thing: keeps half of the planet from freezing solid.
But it means Earth isn’t spherical.
Earth’s equator is spinning around at hundreds of meters per second.
And when a round object spins, it bulges perpendicular to the axis of rotation.
The physics of why that happens, it’s not exactly simple, but it’s something you probably
intuitively understand.
Earth is actually ever-so-slightly squished and fatter near the equator.
Plus, someone standing at the equator feels an apparent force pushing them away from the
center of the Earth, just like one of those spinning carnival rides.
Gravity gets weaker with distance, so–being a bit farther from the center of the Earth
plus that small centrifugal pull makes gravity at the equator about… drumroll please…
0.5% weaker than at the poles.
But!
This bulgy “ellipsoid” Earth isn’t the whole story either.
Earth isn’t a smooth chocolate cake, it’s more like a brownie with nuts.
Our planet has lumps and chunks with different densities that make gravity at the surface
a little different all over.
For example, the crust beneath Iceland and the mid-Atlantic ridge is more dense than
in the Indian Ocean, which means more mass, which means stronger gravity in the N. Atlantic.
When you take into account the actual distribution of matter in the Earth, gravity where you
are may be higher or lower, depending on the kind of rock in the crust under your feet,
or if you’re over water, or even what’s in the mantle below.
Plus, stuff like whether you’re at sea level or on top of a mountain… there’s a lot
to take into account.
So the real earth is a squished, spinning, lumpy, irregular blob with uneven gravity.
But we need precision measurements of these gravity differences in to keep super-sensitive
technology like GPS working right.
We could go around and weigh something on a scale everywhere, but that’s a lot of
work.
Scientists have a way cooler method.
NASA uses two identical satellites following each other on the same orbits.
As the first satellite passes over a spot with higher gravity, its orbit speeds up and
the two satellites pull apart.
When the second satellite passes over that high gravity spot, it also speeds up and closes
the distance.
But if the leading satellite passes over a spot with low gravity, it slows down and the
second satellite catches up a bit before passing over the slow spot itself.
If this sounds like a never ending game of cat and mouse, NASA agrees!
They even named the satellites Tom and Jerry.
Scientists are able to measure the distance between these satellites to the width of a
human hair in order to reconstruct a gravity map of our entire planet.
We’ve mapped differences as small as 0.001% in Earth’s gravity.
These maps show how places like the Himalayas, Andes, Indonesia, all have slightly stronger
gravity, while areas like the Hudson Bay or Indian Ocean have slightly weaker gravity.
So let’s go back to our question from the beginning: Putting all this together, where
on Earth would you, or a kilogram of feathers or steel, weigh the most?
At a spot in the ocean near northern Russia.
The effect of Earth’s rotation making gravity strongest near the North Pole, combined with
some especially dense crust puts Point Heavy right there.
And where on Earth do you weigh the least?
If you guessed the equator, you’re close.
It’s Huascaran, a Peruvian mountain just south of Earth’s middle.
Higher altitude combined with the bulge creates the weakest gravity anywhere on the planet.
But the effect is pretty small.
If you dropped a ball on top of the Peruvian mountain it would only hit the ground 800
microseconds later than it would at Point Heavy, and a 70 kilogram person would only
differ in weight by about half a kilogram.
But if you’re really looking to shed weight thanks to a technicality of physics, it certainly
wouldn’t hurt to try scaling a mountain.
At least you’d burn some calories on your way up.
Stay curious.