The experiment that took place on 29/08/19 at the top of The Hill of Infinity at AOP

Measuring Gravity

As part of a survey to determine the true topography of Ireland by Ordnance Survey Ireland, AOP has recently hosted an experiment designed to measure the Earth’s gravity to an incredible precision, just 10 nms-2! That’s an incredible 0.00000001 ms-2! To put into context just how accurate that is, it’s equivalent to measuring the distance between Armagh and Dublin (about 100km apart) to within about a millimetre.

These measurements were being taken as part of an effort to update the height map of the island of Ireland, along with many other measurements from all over the island. Once all the data has been gathered, it will allow maps to be accurate to within just a few centimetres across the island. The need for these measurements is due to the Earth being a perfect sphere, but instead is covered in lumps and bumps on the surface. This is a problem for cartographers who want a nice neat surface for their maps to be drawn onto.

Earth’s Gravity

While the Earth has a roughly constant gravity of 9.81 ms-2, this varies enough around the globe to be noticeable. For example, if you were to weigh yourself at one of the poles and then again at the equator, you would find yourself weighing a few hundred grams less at the equator due to the centrifugal force will reduce the effects of gravity as you spin around on the equator.

But there are other things that affect how gravity will affect objects at different points on the Earth’s surface. The acceleration of an object due to gravity (g), in its simplest form, is just a relationship between how massive something is (M), and the distance from the centre of the object it’s being attracted to (r), with a constant of proportionality between the two (G). Mathematically, it looks like this:

g  = GM/r2

This means that the more stuff there is beneath you (M), the greater the acceleration, and the further away you are (r), the weaker the acceleration. This is relevant for things like mountains as you will weigh less on a mountain than you would at sea-level. This is because you’re further from the centre of the Earth (you do have more “stuff” in the mountain that adds to the gravity you’ll experience, but this is less important than the height you gain from climbing).  The surface of the Earth is covered in hills, mountains, valleys, and all sorts of things that change how far away from the centre of Earth, so this bumpy surface needs taking into account.

Anomalies of Earth’s Gravity. Image credit: NASA

Another thing that affects the local gravitational acceleration is the local geology. Some parts of the Earth are made of denser, heavier, materials than other parts. This leads to a lumpy gravitational field with some areas having a stronger gravity than others depending on what the ground below is made of. These variations were measured the NASA (and German) Gravity Recovery and Climate Experiment (GRACE) satellites, and the image below shows their results of the anomalies on the surface of Earth.

One of the reasons the bumps in the gravitational field are important is that they affect the way satellites orbit, as they’re sometimes pulled towards the Earth more than usual. It is important to know where these anomalies are and how strong they are so orbits can be accurately measured and predicted.

So between the centrifugal force, the lumpy surface, and the varying composition, gravity is slightly different all over the world.

So how to we measure it in a particular place?

We take the simplest experiment possible: dropping an object to the floor and measuring how long it takes to fall.

The experiment hosted in Armagh takes this idea to a whole new level.

Some of the equipment used for the experiment

The Experiment

With an experiment this precise, everything possible needs to be done to make sure gravity is being measured, and only gravity. Under normal conditions an object will be slowed by air resistance as it falls, so the experiment needs to be conducted in a vacuum. To accurately time how long the object takes to fall, highly precise temperature controlled lasers are used. Even though the drop is only 7cm, the different strength of gravity between the top and bottom of the top of the drop needs to be accounted for. Furthermore, the gravitational influences of the Moon and Sun must also be calculated, and when measurements are being taken to an even greater degree of accuracy, the gravitational effect of other planets (particularly the massive Jupiter) need to be included in the final calculations as well.

To take the prepare the experiment, the drop tube is first evacuated of air using an ion pump, before the equipment is confirmed to be perfectly level using a laser beam. To ensure the measurements are as accurate as possible, the equipment is isolated from the environment as much as it can be to avoid any unwanted vibrations. As it was a windy day in Armagh while the measurements were being taken, the apparatus was protected from the wind by a tent and a wooden windbreak. Despite these steps being taken, the technician running the experiment described how even the wind blowing the trees around was enough to affect the measurements, as the vibrations from the trees would be carried through the ground to the experiment. That shows just how sensitive it is!

Once set up, the experiment was conducted by repeatedly dropping a small ball through the vacuum chamber and using the lasers to time how long each fall takes. Each measurement is very slightly different, so for each run of the experiment 120 drops were made, and 8 runs were performed for a total of nearly 1,000 individual drops. By taking so many measurements and averaging the results, the true value of the acceleration due to gravity at that location can be determined with an incredible accuracy. The more measurements you make, the lower the uncertainty in your result gets.

The results of the experiment

The Results

Armagh has a refreshingly average gravity! After a few runs, the measured value for g was:

gArmagh = 9.814554 ms-2

As the experiment continued to run throughout the day this result will have got closer and closer to the true value for Armagh, and once this has been done all over the island of Ireland the data will be used to compute a new map of Ireland, the accuracy of which has never been seen before.

Article by Tom Watts

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