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GOCE: Gravity and a slightly knobbly earth

There are only four forces in the universe. These forces are responsible for sticking everything together. Without them the universe would consist of a thin soup of minute particles with huge gaps inbetween. Nothing would ever stick together. There would be no such thing as life, or molecules or even atoms. It would be a cold, dark and very dull place.

The four forces are:

  • The strong nuclear force – this sticks atomic nuclei together
  • The weak nuclear force – helps quarks do quarky things
  • The electromagnetic force – this sticks atoms and molecules together
  • Gravity - this sticks planets, stars, solar systems and galaxies together

Gravity is a force of attraction between objects that have mass. Gravity is by far the weakest of the four forces, but you may disagree with this if you fall off a 100m cliff! If you think about it: the gravitational pull of a whole 6,000,000,000,000,000,000 tonne planet can be counteracted by the tension in piece of climber’s rope thinner than a clothes line. Gravity is only strong when masses are really big.

If there were two 250,000 tonne super tankers floting in space their gravity would pull them together. The gravitational force between them would be about 0.042N: the weight of a teaspoon full of sugar on Earth. This force would take about two weeks to pull them together, and they would reach a maximum velocity of about 0.1 mm/sec.

Super Tankers in Space
Table

The further away two objects are the weaker the gravity gets. In fact, the force of gravity falls off quite quickly with distance. If you double the distance between two objects the force of gravity is four times weaker. It never falls to zero though. Every atom in the universe exerts a gravitational force on every other atom in the universe. It is just infinitesimally weak!

The Earth, along with all other bodies that have mass, has a gravity field. Fields are just places where things exist. You will find corn in a corn field; you will find gravity in a gravity field. If the Earth was a perfectly smooth sphere, and made of stuff with a constant density, the gravitational field around it would be perfectly uniform. This, of course, is not so. The Earth is knobbly; it has mountains and ocean basins.

It is also made of lots of different kinds of rocks, and all with slightly different densities. It is also not spherical. It bulges at the middle because it is spinning. The diameter of the Earth at the equator is about 43Km (26 miles) greater than at the poles. This is quite small, but makes an easily measurable difference to gravity. You would weigh about 0.5% more at the equator than at the poles.

The planet Jupiter is much bigger than the Earth and spins much faster: on Jupiter a day is only ten hours long. Jupiter has an equatorial bulge so huge you can see it though a small telescope from your back yard. It is easy to see in photographs.

Mountains and Ocean Basins
Jupiter

Gravity also decreases with altitude. The higher up you go the further away from the centre of the Earth you get. On the top of Mount Everest gravity decreases by about 0.28%. When you are flying in the space shuttle at an altitude of about 400Km (249 miles) gravity decreases by about 10 per cent. There is no such thing as zero gravity. In orbit you are in ‘free fall'; you still weigh 90 per cent of what you do on the surface. It is just that you are falling towards the centre of the Earth at the same rate as gravity is pulling you, along with everything else in your spaceship.

Another thing that has a major effect is geology (the type of rocks present) and the topography (the presence of mountains or ocean basins etc). If you are sitting on top of a lot of very dense rocks, like basalt, they will produce slightly stronger gravity than low density rocks like sandstone. Look at the table showing cities around the world: the difference in gravity (g) is quite striking! Can you think of a reason why Mexico City has a very low gravitational field strength?

Gravitational Spread

The picture shows high gravity areas as red and low gravity areas as blue. The shape of the Earth has been vastly exaggerated to show the effect on its shape.

This local difference in gravity has been used for decades by oil and mining companies' search for valuable deposits of oil, gas or minerals. If you see a very localised drop in gravity you may by over some low-density rocks; these will sometimes contain oil or gas. If you have a high gravity anomaly you may be over a rocks containing high-density material like iron ore or even gold! This can be a really useful technique when combined with other data.

So what is GOCE all about?

GOEC is the ‘Gravity field and steady-state Ocean Circulation Explorer’(GOEC) satellite. Its job is to map the gravity field of the Earth in incredible detail. If you look at picture of GOCE we can see straight away that it looks very different from any other satellite. This is because it is streamlined! GOCE is a 5m long, one tonne arrow. It is designed to orbit at a very low altitude of only 263Km (163 miles). The International Space Station(ISS) orbits at 350Km (218 miles), and this is generally considered to be a very low-earth orbit. GOCE's orbit is incredibly low for a satellite and means it is actually orbiting within the top of the Earth’s atmosphere.

This is why it needs to be streamlined. It is also moving very fast, nearly 18,000 miles per hour (8Km/sec), or about ten times the speed of a rifle bullet. At these sorts of speeds even very, very thin air can produce a lot of drag. In fact, GOCE makes use of the thin air by having tiny steerable winglets that are used to keep its position stable. It also has a revolutionary electric motor to help keep it in orbit: an ion drive. GOCE need to be low to get a strong gravitational signal. Remember gravity gets weaker with distance.

So how does GOCE measure gravitational field strength?
GOCE Orbits

It uses two methods. The first measures quite large changes in gravity. This uses GPS satellites to track the position of GOCE itself. GPS satellites fly in very high orbits about 20,000Km (12,427 miles) above the Earth’s surface. This allows them to look down on GOCE and track its position very accurately, just like a car sat nav. As GOCE obits the Earth it shifts slightly in its orbit depending on the gravitational pull of the Earth. These movements can be used to calculate the gravitational field strength.

The second method is a bit more complicated. It uses three pairs of masses joined by fine springs. As the gravity field changes, the masses, only about 0.5m apart, experience slightly different gravitational pulls and the spring stretches by a tiny amount. Lasers are then used to measure this stretch and work out the change in the gravitational pull. The lasers can measure the stretch of the springs to about one picometer. This is a lot less than the diameter of a typical atom. The system is so sensitive it can detect a change in the gravitational field strength of 0.000001 N/Kg.

This is so amazingly sensitive that it can even detect the presence of ocean currents by being able to ‘see’ the different density of the sea water when it’s just a few degrees warmer or cooler than the surrounding water. Understanding how the oceans move heat around the planet will help improve the computer models that are used to forecast global climate change.

GOCE is one of squadron of satellites known as ‘the Earth explorers’ that are being launched by ESA (The European Space Agency):

  • Smos will study the saltiness of the oceans
  • Cryosat-2 will map the Earth’s ice
  • Aeolus will use a special laser to map and measure the planet’s winds
  • Swarm consists of three separate satellites that will monitor the Earth’s magnetic field
  • Earthcare will study how clouds form and what effects they have

By combining data from all these spacecraft we may really start to understand the future of climate change and be able to prepare for it.

Project

Your task is measure the gravitational field strength as accurately as possible in a school lab. Hint: think light gates and pendulums to start with. There are many different ways of achieving an accurate result. Send us a video or still picture of your set up and your reading for gravity!

The big questions:

What forces hold the universe together?

Is gravity constant on the Earth?

How can measuring gravity accurately be useful?