If you’re looking for a guaranteed  way to lose a little weight, you could head to the middle of the Indian Ocean.

Without any change to your exercise or diet, you’d stand on a scale in Sri  Lanka and be a few grams lighter! This isn’t caused by any changes to your mass, but rather by how much  gravity you’re experiencing.

The strength of gravity at the Earth’s  surface varies depending on where you are. And yeah, a few grams might not seem  like much on the scale of a person. But when you get to the scale of the  Earth, it can make a pretty big difference.

If you prefer a colder  climate, there’s also a giant, moving gravity hole under Antarctica. It might even be the reason  the continent froze over! And the thing is, scientists still aren’t  entirely sure why these holes are there at all. [♪ INTRO] Look at any picture of Earth from  space and you’ll see a sphere.

But the Earth isn’t really a sphere. Way back in 1687, Isaac Newton  suggested our planet is both slightly flattened at the poles  and fattened at the equator, on account of the forces  generated as the Earth spins. And by the 1730s, careful measurements  confirmed that on a broad scale, the Earth is an ellipsoid.

Unfortunately, for many practical purposes, saying the Earth is an  ellipsoid also isn’t enough. Obviously, when you zoom way in, you’ve got the changing relief  of mountains, valleys and oceans. But there’s something else at play, too.

In 1828, German mathematician  Carl Friedrich Gauss was trying to accurately map and measure  his native kingdom of Hanover, so the government could work out  how to tax everyone properly. Of course this all started as a way to make money. He used triangulation and plumb  lines to level his equipment, but over large distances, the  triangles he drew didn’t match up.

This led Gauss to propose a new,  purely mathematical definition for the Earth’s shape, called  its equipotential surface. Just like the term “equidistant”  describes points that are all of the same distance from a reference point, the term “equipotential”  describes points that experience the same gravitational force as each other. On the Earth, objects experience gravity  pulling stuff towards the center, and a centrifugal inertial force  throwing stuff outwards due to rotation.

So the equipotential surface is the place  where these two things are balanced. It’s a theoretical surface  that wraps around the Earth, where if you placed a marble it  wouldn’t roll in any direction. Another way to think of it is  that it’s the shape the oceans would take if they were completely  calm, with no waves or tides.

Water is pulled down by gravity, and bulged out near the equator by the  centrifugal inertial force. So practically, the equipotential  surface defines the mean local sea level. Fifty years after Gauss,  another German mathematician coined the friendlier word geoid to  describe this theoretical mean sea level.

Now, if the world worked according  to Newton’s mathematics alone, the geoid would be a smooth,  featureless ellipsoid. But it’s a bit more complicated than that. Gravity is linked to mass.

And more mass means more gravity, so  wherever you have big lumps of stuff, you get slightly more gravity  than when you have less stuff. But ultimately, density is the  thing that matters, and on Earth, there are a lot of things that  can create density variations. Ice is less dense than water,  which is less dense than rock.

Continental crust is less  dense than oceanic crust. And hot rocks and magma are  less dense than cooler rock. Each of these features on  or inside the Earth creates what geologists call gravity anomalies, where the gravity reading is higher  or lower than we’d expect it to be if the earth was one homogenous blob.

And these anomalies create  so-called geoid undulations, which are literal height differences  from the idealised ellipsoid. So it might be a mathematical surface, but the geoid does physically  affect the height of the oceans. Where gravity is higher beneath the surface, water is pulled towards those  areas, creating higher sea level.

And where gravity is lower, there’s  less pull compared to other areas, so sea level drops, creating  a literal hole in the ocean. Even though the concept of the geoid  was established in the 19th century, it was actually a long time before we  had a way of accurately measuring it, because it requires a lot  of very precise measurements made on the scale of the whole planet. You can do it by hand, using a combination of astronomical and earthly measurements.

But the big leap in ability came  with the help of satellites. LAGEOS, launched in 1976, takes the prize  for the funkiest of all satellite designs. It had no electronics or moving parts.

It was basically just a giant golf ball  with angled mirrors in each of its dimples, like a cosmic disco ball. Ground stations would shoot  lasers up to it and the mirrors would reflect them back, and the  return time would tell scientists the precise distance to the satellite. And that distance would change according  to the variable pull of gravity on Earth, like the geoid projected into space.

Then, in 1992, the TOPEX/Poseidon  satellite was able to map the geoid itself, by sending radar signals down from  the satellite to the ocean surface to “see” the geoid undulations. And since 2000, there have been  multiple pairs of satellites that each have one satellite measure  gravity’s effects on the other. Thanks to these instruments, we now have a great high-res map of our planet’s geoid.

And one of the most famous representations  of it is known as the Potsdam potato, named after the German center for  geosciences that put it together. Even after 200 years, Germany is still  the place to go to understand gravity. And just like all that science,  we need funding to keep going.

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You can upgrade to Premium to unlock all courses. And right now, SciShow viewers can save 20% off an annual subscription  at brilliant.org/scishow The Potsdam potato reshapes the  surface of the Earth to its geoid, to show where the gravity highs and lows are. In reality, the anomalies  are nowhere near this big.

They’re often far smaller than  the real hills and valleys that shape our planet’s surface. But the visualisation helps to show  just how varied the geoid can be. And scientists haven’t gone to all this effort  over the decades just for the fun of it.

Knowing the precise shape of the geoid is  critical for making GPS actually useful. Because satellite-based GPS calculates  your position using pure geometry, and maps it to the ideal ellipsoid. But in places where there  are big gravity variations, the altitude can be off by a significant amount.

So a second calculation built into  the system adds in the information from the geoid, correcting the altitude  relative to the real local sea level. But having a picture of the geoid is  also a window into the Earth’s insides. By comparing geoid measurements  with geological features, geoscientists can map density differences  in places our drills could never reach, helping us to understand what’s  going underneath the surface.

Interestingly, gravity  anomalies don’t always line up with the landscape in the way you might expect. For instance, massive mountain ranges are  a big lump of extra stuff on the surface, so you’d imagine they'd create more gravity. But they’re actually made of  low-density continental crust, and often have deep roots that displace the higher density mantle underneath them.

As a result, the biggest mountain  ranges like the Himalayas actually correspond to a negative gravity anomaly. A small gravity hole. Instead, the highest gravity hills on the geoid are found where there’s a surplus of  dense material beneath the surface.

There’s a significant high around  Iceland, in the middle of the Atlantic, related to the thickening of denser oceanic  crust that breaches the surface here. Another geoid high is located  in the Western Pacific, centered on Papua, New Guinea. A combination of factors contribute  to its higher than average gravity.

It’s a place where oceanic  tectonic plates are colliding, so you’ve got a thickening of dense crust, plus an excess of dense mantle  material near the surface. But the volcanic arc setting also means newly created oceanic crust is piled on as well. This shows there isn’t always a clear  recipe for high or low geoid undulations.

Another case in point is  the Indian Ocean Geoid Low, the commonly cited lowest  point on the entire geoid. Centered just over the tip of India, the  geoid is 106 meters below the ellipsoid. And it’s not only the deepest, but also  the largest gravity hole on the Potato, spanning more than 15,000 kilometers in diameter.

Scientists still aren’t  entirely sure why it exists. Without anything obvious on the  surface, there must be some seriously low density stuff going on within Earth’s mantle… that massive layer of rock beneath the crust. One option is there’s something  called a slab graveyard at the bottom of the mantle that’s  so big and heavy it’s pushed the core-mantle boundary down,  displacing the even denser outer core below the mantle, while  simultaneously sending a plume of less dense hot mantle material upwards.

Unfortunately, the image  resolution this deep in the Earth just isn’t good enough to say for sure. But the Indian ocean isn’t the only place  you’ll find yourself light on your feet. There’s another gravity hole,  under the Ross Sea near Antarctica.

And according to a study published in  2025, this one’s been getting deeper. The scientists behind that  study used earthquake waves to scan the interior of the planet, just  like we use sonar to map the ocean floor. This produced a deep earth density map that closely matches the distribution  of gravity anomalies.

Just like in the Indian ocean, it looks  like the lower gravity in Antarctica is caused by a combination of crustal  slabs sinking to the ocean floor, and hot plumes closer to the surface. But their study also revealed  something surprising: Antarctica’s hole was on the move. With their reconstruction of  the deep mantle in this area, they ran a simulation that showed how the density and gravity anomalies changed over time.

Apparently, this gravity hole has existed  for at least the last 70 million years, but between 50 and 30 million years ago, it strengthened and migrated from the  south Atlantic to where it is now. The scientists suggest this  happened as a result of the hot plume underneath  Antarctica becoming stronger. And in fact, it represented such a big  movement of mass within the mantle, that it was enough to shift the  entire planet’s axis of rotation.

Coincidentally, this shift also coincides with the timeline for Antarctica freezing over. The team suggests this gravity  hole may have played a part. Lowered gravity means that water  moves away from the region to areas of higher gravity, pulling the local  sea level down to a lower level.

This, in turn, exposes more  of the continental shelf, which alters ocean currents and weather systems, and which may have contributed to Antarctica’s climatic isolation and the growth of ice sheets. In all, the measurement and  understanding of geoid undulations is a pretty young science, despite  its long theoretical foundation. We’ve not yet had a chance to see how  much or how fast these gravity hills and valleys move, but this Antarctica study  hints at the importance of finding out.

Our planet’s lumpy potato may not  be a reasonable weight-loss plan, but it sure is useful. [♪ OUTRO]