document: The Geoid : Why a map of Earth 's gravity yields a potato-shaped planet This video is no April 's fool joke : Earth really is shaped like a potato . However , the shape that you see here is , um , slightly exaggerated to highlight its irregularities . Another caveat : what is depicted here is not the shape of the planet , but rather the shape of an idealized sea-level surface extending around the entire globe -- a surface that Earth scientists call the geoid . The video is the most accurate reconstruction of the geoid to date , and was released by the European Space Agency at a scientific meeting in Munich on March 31 -LRB- see a video of the related press conference here -RRB- . It is based on data collected by ESA 's Gravity Field and Steady-State Ocean Circulation Explorer -LRB- GOCE -RRB- . The five-meter long , arrowhead-shaped probe has been in a low orbit for almost exactly two years , collecting painstakingly accurate measurements of the gravitational field of Earth . Alas , many of the Web sites and blogs that reported on GOCE 's results so far got it wrong . Contrary to what was stated in these reports , the geoid is not a surface on which the strength of gravity is the same at every point . The geoid is , in the words of an oceanographer on the GOCE team , a surface such that if you placed a marble anywhere on it , it would stay there rather than rolling in any direction . Another way of saying it is , imagine you were an engineer traveling around the world with a level . Then wherever you go , the level would be exactly parallel to the geoid at that place . Yet another equivalent definition : it is a surface that 's everywhere perpendicular to the direction of a plumb-bob , or in other words , to the gravitational field . Gravity need not have the same strength everywhere on the geoid . In other words , if you could walk on the geoid you would see gravity always pointing exactly downwards , but your weight could slightly change from one region to another . The misunderstanding may have stemmed from the confusion of two concepts from multivariable calculus : a vector field and its potential . The vector field in this case is the gravity field , and the potential is the gravitational potential -LRB- which is essentially the gravitational energy of a unit mass -RRB- . At any point in space , the gravity field can be seen as the direction in which the gravitational potential rises fastest . Its magnitude , or length , is the rate of change of the potential . The field defined this way is called the gradient vector field of the potential . In general , the gradient of a quantity defined in space is the 3-D version of the derivative of a quantity in the sense of single-variable calculus . -LRB- To be pedantic : for historical reasons , the gravity field is defined to be the opposite vector to the gradient of the potential . -RRB- If you were to follow a gravitational field line -- a curve which is at every point tangent to the vector field at that point -- you would follow a curve of steepest ascent on the gravitational potential . That 's why it is called the gradient . -LRB- Note that because of inertia , the field lines of the gravitational field are not necessarily the trajectories of a body in free fall . The field wo n't tell you in which direction you 'll be moving -- only in which direction you will accelerate . -RRB- Gradient vector fields are difficult to grasp in 3-D , because picturing the potential -LRB- to visualize the ascent or descent -RRB- would require a fourth dimension . But a 2-D analogy might help . Think of how water trickles down a hilly surface . Neglecting inertia , a droplet of water would follow a curve of steepest descent , which is a vector field made of vectors along the surface . In this analogy , the elevation of the droplet is the analogue of the potential at that point . And the analogue of the geoid is an elevation contour on a topographical map : the potential -- the height -- is constant along the contour . Obviously , some parts of this contour can be on steep terrain , whereas others can be on mild gradients . -LRB- On a topographical map , the slope is steeper where many different contour lines are crowded together . -RRB- The magnitude of the gradient vector field -- which represents the steepness of a slope -- is not the same at all points of the contour . Thus , gravity does change in strength along the geoid , and so the geoid is not '' `` a shape where the gravity is the same no matter where you stood on it , '' '' as one blogger put it . Nor is it '' `` how the Earth would look like if its shape were distorted to make gravity the same everywhere on its surface , '' '' as reported by a major news site , which went on to add that '' `` areas of strongest gravity are in yellow and weakest in blue , '' '' apparently not noticing the contradiction with the previous sentence . There are many reasons why the geoid is n't a sphere . First and foremost , the Earth itself is n't a sphere . It is closer to an ellipsoid , being flattened at the poles by the centrifugal force of its own rotation . But the planet is n't an ellipsoid either , because of topography . Mountains and valleys are asymmetrical distributions of mass . That mass distribution affects the gravitational field and makes the geoid asymmetrical too . Then there is Earth 's inner and outer structure . The oceanic crust and the landmasses of the continental shelves are made of different materials that have different densities ; and farther down , the mantle is not uniform either , with regions that have slightly different compositions and temperatures , and thus slightly different densities . '' `` The variations , '' '' Reiner Rummel , a senior GOCE scientist , told me in an email , '' `` reflect processes in the deep earth mantle such as descending tectonic plates and hot mantle plumes . '' '' All of which affects the strength of the gravitational field , and the GOCE 's orbit . The probe measures these effects thus it measures the gravitational field . The geoid is not to be confused with anomalies due to the topography of the land -- although it is affected in part by it . Also -- and here is where things get really tricky -- it is not to be confused with the actual sea level . Wait a minute , you say , but is n't the ocean supposed to be at sea level by definition ? Except for relatively small perturbations such as waves or tides , you say , should n't the surface be exactly horizontal -LRB- that is , perpendicular to the gravitational field -RRB- everywhere ? Is n't that , after all , what '' `` sea level '' '' means ? Yes , to some approximation . However , the oceans are not homogenous . Differences of salinity and temperature make them more or less dense . Moreover , the Earth 's rotation produces forces that keep the oceans in constant motion . Just like the water in a river is not all at the same level -- after all , it flows to the sea for a reason -- the water in the ocean also has differences in height . And by height , it should be clear by now , I mean elevation relative to the geoid , which can be positive or negative . Oceanographers thus speak of the '' `` topography '' '' of the ocean , meaning that it really has hills and valleys . In fact , here is where the '' `` ocean circulation '' '' part of GOCE 's name comes into play : one of the main goals of the mission is to measure the oceans ' topography and from that deduce the structure of the oceanic currents . The deviations of the geoid from the simplified , ellipsoidal model of the Earth are substantial : they range from 100 meters below -LRB- dark blue in the video -RRB- to 80 meters above -LRB- yellow -RRB- , Rummel says . The surface in the video is the geoid amplified by a factor 7,000 , says GOCE mission manager Rune Floberghagen .
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