Where the same person weighs least in Romania, on the same bathroom scale

Your place, on the scale

Enter your weight in kilograms and pick a place, on the map or from the list. The result shows what a spring scale that reads exactly that weight in Constanța would read there, and what the difference is made of: latitude, height, the rock below and the air. Above the ground, the climb goes up to airliner height.

The whole country, in grams

The computation covers 10,955 points inside the country. A typical point sits at +5 grams against Constanța, and 75% of points stay between −10 grams and +10 grams. The broad pattern is simple: the southern mountains pull weakest, the northern plain strongest, and in between the differences grow steadily with latitude and shrink with every hundred metres climbed. The thinner mountain air softens the height difference by about a third. The heaviest computation point falls at the country's northern tip, near Darabani, at +24 grams; the lightest places are the Bucegi summits in the table.

30 named places, lightest to heaviest

Why the needle moves

Four things move the needle, in order of strength in Romania: how high the place is, how far north it is, how thin the air is, and what rock lies underneath.

The spring scale and the balance

The whole story hangs on the instrument. A bathroom scale with a spring or a force sensor measures the pull of the place, so its reading changes on the road. A balance with counterweights, like a pharmacy beam, compares the body with known masses in the same pull: both pans feel the change in gravity alike, so it cancels. Only the air is left: steel weights take up eight times less room than the body and the air holds them up less, so, carried up Omu, the balance reads about 16 grams more. The body's mass stays the same everywhere; what changes is only what one kind of scale says about it.

One more detail, kept to scale: the Moon and the Sun raise and lower the solid ground twice a day and, with it, the pull of the place, but on the display the movement stays under a tenth of a gram at 70 kilograms. The ground's own motion is the subject of the page on the tide in the stone.

For weights of another order: what built Romania weighs puts 4.43 billion tonnes of buildings, roads and railways on the scale, and pocket gravity lets a finger pull at orbits.

How it was computed, and where the evidence stops

Local gravity comes from the EGM2008 global model, built from satellite, land and marine-altimetry measurements, evaluated here from its published coefficients to degree 1,080 (features down to about 20 kilometres), right at the ground surface. A summit, though, is a point and the model is smooth: for the named places and the summits, the pull of the terrain finer than the model is added, worked out from the Copernicus GLO-30 elevation model (30-metre cells) against its own 10-arc-minute mean. Each summit sits on the highest point of the elevation model, within 40 metres of the height printed on maps, and every summit above 2,380 metres in the Southern Carpathians was worked out the same way, so that the lightest place does not hang on a hand-picked list. Map-point heights come from the Terrarium terrain tiles (SRTM data). The split uses the normal gravity of the GRS80 ellipsoid: the latitude part is the difference in normal gravity, the height part its decrease with altitude, and the remainder belongs to the rock. The air part uses the International Standard Atmosphere and a body about as dense as water, 70 litres for 70 kilograms.

A second computation, written separately in another programming language, reproduces the model's gravity at the named places within 0.2 grams. With a second global model, XGM2019e, or with EGM2008 to degree 2,190 and the fine terrain taken against its 5-arc-minute mean, the named places move by at most 4 grams: Omu comes out between −17 grams and −19 grams, and Moldoveanu stays 4 grams to 6 grams heavier. Without the air, from gravity alone, the difference from one end of the country to the other would be about 60 grams. The printed numbers are differences between places; an absolute reading would depend on where the scale was set at the factory.

Sources

• Pavlis, N. K., Holmes, S. A., Kenyon, S. C., Factor, J. K. — The development and evaluation of the Earth Gravitational Model 2008 (EGM2008), Journal of Geophysical Research (2012). doi.org/10.1029/2011JB008916 · coefficients via ICGEM, GFZ
• Zingerle, P., Pail, R., Gruber, T., Oikonomidou, X. — The experimental gravity field model XGM2019e, GFZ Data Services (2019). doi.org/10.5880/ICGEM.2019.007
• Heights: Terrarium terrain tiles from the AWS open-data archive and the Copernicus DEM elevation service via Open-Meteo. registry.opendata.aws/terrain-tiles · open-meteo.com
• Fine terrain and summits: the Copernicus GLO-30 surface model (30-metre cells), © DLR and Airbus, provided under the Copernicus programme of the European Union and ESA. spacedata.copernicus.eu
• Air: the International Standard Atmosphere (ISO 2533).
• Country outline: Natural Earth first-order administrative units, 1:10 million scale. naturalearthdata.com
• GRS80 normal gravity: the Somigliana and Moritz formulas, summarised in the ICGEM documentation. icgem.gfz.de/theory