3.20 Gravity part 1: gravitational force and the solar system

“I’ve always been fascinated by gravity” admitted Helen unexpectedly in a discussion one day. “it’s so different – it’s extremely weak, yet it’s effects in the universe are so big!”. With her background in the Arts, Helen was captivated more by its pervasive yet invisible presence than by its mathematical formulation. Celia, a theatrical agent, who had missed out almost entirely on science at school, announced that she couldn’t see it as a force at all. “It seems ‘too negative’ a thing to be called a force. It just lets things happen passively – it just makes things fall. It’s like an absence of something” she explained.

This search for an intuitive feel for gravity opened up an interesting discussion, far removed from the dry lesson on Newton’s Law of Gravitation that had been my introduction to the subject. The starting point was sheer wonder at this intangible super force. Questions and speculations flowed. “It‘s symmetrical around the Earth, but is it stronger or weaker in the interior?”. “If you go to the edge of space, like a balloonist, is it still there?” “Do gas planets have a gravity pull or is it only solid ones, like Earth?”

Gravity and mass

The most fundamental point about gravity is that it is a force that acts between physical objects simply due to their mass: that is to say the amount of matter that makes up objects, rather than their shape or the nature of the substance of which they are made. A kilogram of balsawood and kilogram of lead each exert the same gravitational pull (though a kilo of balsawood would be much bigger, of course). However, the force is so weak that it is effectively undetectable between everyday things like me and you, tables and chairs. But for massive objects it is measurable.

A famous experiment to prove this was undertaken in 1785 by the Astronomer Royal, Nevil Maskelyne. He placed a pendulum on either side of a symmetrical mountain in Scotland called Shiehallion and with sensitive instruments was able to measure the very slight deflections from the vertical.

Figure 1 Schiehallion mountain in Scotland. Image credit: Andrew2606 at English Wikipedia

The mass of the mountain was attracting the pendulum bob sufficiently to deflect the pendulum by about ten seconds of arc (i.e. about one 360th of a degree) – not a lot, but enough to confirm Newton’s theory of gravity, and to enable the mass of the Earth to be estimated, as well.

Figure 2: Deflection of a pendulum by gravitational pull of a mountain. Image credit: Billc

If a single mountain can attract a small pendulum bob detectably, we can easily imagine how an object the size of the Earth attracts things significantly. This is what we learn reluctantly at school to explain why people in Australia don’t fall of the ‘bottom’ of the globe. We are all attracted towards the centre of the Earth by the gravitational attraction of this massive object. That’s what keeps us all planted firmly on the ground.

In everyday life we hardly notice this ever-present force pressing us down on the Earth (except when our feet ache and we want to ‘put them up’). Walking on a sandy beach or bouncy castle, however, teaches us an important property of gravitational force: its dependence on the amount of mass. A small child leaves fainter footprints than a burly adult. The force we exert down on the ground depends directly on how massive we are. It’s this very fact that enables weighing scales to record the force pulling us down towards the centre of the Earth – what we call our weight. A 100 kg person presses down on the Earth with twice the force of a 50 kg person.

Everyday objects are, of course much less massive than the Earth, so the gravitational force between them is entirely negligible. The overwhelming mass of the Earth, however, means that the force between itself and everyday objects – their weight – is significant here on Earth. The Moon is, of course, smaller – less massive – so it pulls less strongly on objects. We say the gravity is weaker and things weigh less. If we could take an object up to the Moon, it would weigh less there – around one sixth of its weight on Earth. We see this in the film of astronauts walking on the Moon – bouncing strangely high with each step.

These simple facts illustrate one of the important properties of the gravitational force. It’s clearly stronger the more massive each object is. A child weighs less than an adult because it has less mass. They’d both weigh less on the Moon, because the Moon’s mass is less than that of Earth. The force of gravity depends directly on the mass of each object involved –  child, adult, Earth, Moon.

Stars and planets

The examples we’ve considered thus far involve relatively small things interacting with overwhelming massive ones. The gravitational attraction in each case – child . adult, table, chair – is almost entirely due to the massive object – planet or moon. Out across the universe, however, lie many billions of massive objects: stars, galaxies (huge collections of stars) and black holes, for example. They can exert a huge gravitational influence on each other.

In our own vicinity, the Sun and the planets surrounding it are relatively close, on the scale of the universe. The gravitational force between them keeps the solar system intact. Were it not for the force of attraction due the huge mass of the Sun, the Earth and every other planet would fly off at a tangent like a stone from a sling.

Gravitational force has given the universe its form and is central to its activity. Stars, and the planets that surround them, were themselves formed by the gradual coming together of clouds of dust and hydrogen gas pervading regions of the universe. Small though these particles may have been individually, added together their mass was sufficient for gravitational force to aggregate them over time. The forerunners of today’s planets formed as these tiny primitive components began to collide and merge. Ultimately gravity ensured the growth of these so-called planetesimals into the gaseous and solid members of our current solar system.

For Jean the idea of gravity operating on tiny objects like dust particles, and even on gases seemed bizarre. “h=How big does something have to be to experience gravity” she asked. There is no lower limit: any object will experience a force of attraction to every other object in proportion to their masses. Everything influences everything else gravitationally. The Moon exerts a bit of a wobble on the Earth, as it rotates about it. The universe is an infinitely complex set of interactions between all the billions of masses of which it is composed.

As it happens, the universe is not a perfectly smooth soup of particles, spaced out evenly everywhere. Instead, matter has clumped together over the aeons, into the larger entities we know as planets, stars and galaxies (even super galaxies) and these lumps in the universe are extremely far apart from each other. Thankfully, this enables us to make sense of the infinite complexity in which every object attracts every other object. It’s mainly the influence of the huge masses – the stars – on other smaller ones – planets, moons and clouds of dust – that shapes our universe.

This brings us to the second key feature of gravitational force: how it weakens with distance. The further apart two objects are, the weaker is the gravitational attraction between them. In fact the strength of the force diminishes rapidly – as the square of their separation, much as the brightness of light does. Twice as far apart, four times weaker. Thus, for example, the planets are effectively kept in place by the pull of the Sun alone because the next star in the universe is thousands of times further away – hence millions of times weaker. There’s a limit to how distant a planet can be from its dominant star, simply because of the weakening of the gravitational attraction between them with distance. That’s why our solar system for example, has just a handful of planets and a finite size.


Paul in a discussion about gravity and the planets brought up a problem that was baffling everyone. If all objects are attracted to one another simply because of their mass, why doesn’t the universe just implode – all the stars and planets zoom together into one gigantic mass?  Instead we see giant objects like planets and moons circling round bigger objects. “Why are they always orbiting?” he asked.

It’s a challenge to imagine what happens to objects in outer space, where there is no solid surface to offer friction, no air to resist motion, no gravity to give a sense of up and down. Instead, all directions are equal, all motion unresisted. Any object given a kick will just keep going indefinitely, unless by extreme chance it happens to head towards another planet or star in the sparsely populated universe. As you may have noticed when you throw anything, it’s extremely unlikely that you will avoid setting it into a spin. You’d have to push it dead centre to get it to travel forward without any spin. Think frisbee, or cricket ball. 

Objects in space never were still. Nothing in space is. In fact as Einstein pointed out in his Special Theory of Relativity, there is no absolute frame of reference anyway by which you could determine that something was stationary – no such thing as ‘the ground’ out in space. All things are moving relative to one another. We now believe that all the material in the universe was thrown into motion originally by the Big Bang event that brought the universe into being. Long after that, subsequent events have seen stars forming, then growing and ultimately exploding with the ejection of great chunks of matter out into space at enormous speeds.  Each of these explosive moments would have sent matter spinning as well as moving outwards. For this reason, the material that gradually came together to form stars, with their planetary systems, was always gyrating as well as moving ahead: it had both linear and angular momentum, in technical terms. As this matter – the dust and gas molecules encountered earlier – gradually drew together through gravitational attraction, its spinning motion tended to speed up rather then dissipate. It’s an inevitable effect, seen whenever a spinning ice skater draws in their arms to achieve a dizzying speed. The dust and gas that will become a planetary system began to rotate at increasing speed around the star at its centre as the protoplanets began to form. They too start spinning around their own axes. As the rotation of the whole planetary system speeda up, the material in it – dust, gas, protoplanets – gradually flattens, like sloppy clay on a potter’s wheel. Eventually the planets that grow out of this swirling mass end up lying in a single flat plane, all spinning the same way round, as they do in our local solar system.

Figure 3. Solar system showing the planets all lying in a plane

This story, about the nature of gravity and how it has given rise to the solar system with its orbiting planets, gives plenty of food for thought. It’s a serious intellectual challenge to imagine that a force can be exerted invisibly over enormous distances with no intermediate structure or substance. Isaac Newton himself, over four hundred years ago, wrote “that one body may act upon another at a distance thro’ a Vacuum, without the Mediation of anything else, … is to me so great an Absurdity”.

For readers who would like to look at further ramifications of gravity, part 2 describes its role in the formation of stars and introduces Einstein’s differing theory of gravitation.

Click here: 3.21 Gravity part 2: star formation and Einstein’s alternative concept

© Andrew Morris 20th May 2022