Observing the shape of the Earth

A few weeks ago, I visited a dear friend of mine at the University of Kiel. He is a professor in geosciences over there. He invited me to meet his team and learn about what they are doing. It was a great week with lot of learning moments. I advise every PhD student and scientist to once in a while visit other groups in your field to see their point of views. Also, it is nice to get out of your office and see the world. 

I want to write about one particular learning moment that week, which was a field tutorial with the LaCoste-Romberg gravimeter. This particular device is able to measure relative gravity variations up to 10 microGal. That is a relative variation of 9 digits after the 9.81 m/s^2 (in the Netherlands). This is the domain where you can feel the pull of the Moon, when it is orbiting above you. Wow!!!

The Lacoste-Romberg gravimeter in the field. 

The LaCoste-Romberg was invented already in 1932 by Lucien LaCoste and his teacher Arnold Romberg, who'd came up with a complete mechanical way to measure the gravity field. Inside this temperature-controlled box a bar with a proof mass is suspended with wires and springs. I have sketched this during my coffee break, with the forces acting on it. It was a long time ago, I had to solve a static problem and my drawing skills are not perfect.

The mass is held up by an inclined spring and two horizontal wires, such that its rotation point is moved towards the location where the horizontal wires are attached. This clever mechanism increases the sensitivity of the device by the square root of two. The bar with the mass is balanced by pulling or relaxing of the inclined spring, which can be done by rotating a millimeter screw on top of the device (the grey round nob in the first figure). If there is a difference in gravity between measurement stations, this can be observed by the difference in relative rotations of the grey nob.

According to the people at the university in Kiel, the LaCoste-Romberg is one of the most precise instruments to take outside and measure the gravity field of the Earth. So, me being a gravity scientist (artist or nerd, whatever), of course I wanted to try this out. One of the undergraduate students took me outside in the 'field'. There is an abandoned railway track close to the department of geosciences in the campus of the university of Kiel. The railway track is quite flat (only 3 meter difference between station 1 and station 12) and runs north south. This is ideal to measure the curvature of the Earth, or even more precise the parabolic shape of the Earth. Some readers of the blog could remember this post, where I showed a way to measure this, but my pendulum setup was not accurate enough. If I wanted to see the shape I needed to visit the north and south poles. However, now I had a much more accurate device, so was it possible to see the shape of the Earth?

The measurement campaign in Kiel, which runs almost perfectly north south. We walked towards the south so we would see a decline in the measured gravity signal.

In total, we observed the gravity field on 12 locations along a 1-km north-south track. I measured the location of the station with my GPS-device, which was a few meters accurate. The gravity measurements of the LaCoste-Romberg were corrected for tidal accelerations, rotation of the Earth, and the drop of 3 meter in the height of the stations. The measurements could be improved by also correct for drift in the device (forgot to do a benchmark, but we assumed little to no drift within the hour of the campaign) and letting the measurements be done by one person, but this was a tutorial, so some mistakes were made. However, we can still see a shift in the observed gravity field.

The results of the campaign in Kiel: (a) the absolute gravity of the measurements (red) and a the WGS-84 gravity model (black), (b) the relative gravity measurements (red) and a linear fit with uncertainties (blue) compared to the WGS-84 gravity model (black), and (c) the location of the stations in north-south direction.

We have equalised the absolute gravity of station 1 to the WGS-84 gravity model at that location, because the LaCoste-Romberg is a relative gravimeter. Both in the measurement as in the model, a declining trend is visible towards the south. The Earth is not perfectly round and thus you will move farther away from the center of gravity if you walk towards the equator (south on the northern hemisphere). The law of newton states that gravity will diminish if the distance becomes larger. Both the linear trend of the measurements and the gravity model show this behaviour. So finally, I have measured the shape of the Earth and had already proven that the Earth is not flat (see here), but now also that it is not perfectly round.