Perspectives on Gravity

Gravity is such a familiar force that its utterly mysterious nature can sometimes go unnoticed.

Looking at the picture of Earth and Moon bound together in the solitude of the Universe, it is strange to think that all that holds them together is this apparently weak force.

In this article I will do a couple of calculations using Newton’s law of Universal Gravitation. If you know the maths, please check my calculations, and if you don’t, please trust me.

Not so weak

Many people are familiar with the fact that the average gravitational field strength at the surface of the Earth is approximately 9.8 newtons of force for every kilogram of mass. This is sometimes called one ‘g‘.

(This is sometime expressed as 9.8 metres per second per second, but I don’t think that formulation is as clear in this context.)

But what is the gravitational field strength due to the Earth at the Moon? A simple calculation shows it to be just 0.0027 newtons per kilogram – about 0.02% of g.

And yet this weak field is sufficient to bind the Moon to the Earth with a force of 2 × 1020 newtons.

If gravity disappeared (!) and we applied that force to the Moon with a tensile steel cable, it would need to be 1000 km in diameter and would require about half the mass of the Earth to manufacture!

So weak

Many people are familiar with the fact that the tides on Earth are affected by the Moon.

We can work out the gravitational field strength on the side of the Earth nearest the Moon – where the Moon’s gravity opposes the Earth’s gravity: 9.8134727 newtons per kilogram.

Compare this with the gravitational field strength on the side of the Earth farthest from the Moon – where the Moon’s gravity acts with the Earth’s gravity: 9.8134749 newtons per kilogram.

The gravitational field strengths differ by just 0.2 parts in a million. And yet this difference is sufficient to affect the tides!

So very weak

Many people are familiar with the fact that the Earth is bound to the Sun by gravity. And that the Sun is bound to the Centre of the Milky Way Galaxy by gravity.

We can work out the gravitational field strength at the Earth due to the Sun. It is just 0.0059 newtons per kilogram or about 0.06% of g.

And the gravitational field strength at the Sun due to the Galaxy is a breathtakingly small 0.000000002135 newtons per kilogram or just 0.2 parts per billion of the gravitational field strength at the Earth’s surface.

And the lesson is?

There is no lesson here – it is just surprising to me how weak gravitational fields – billions of times weaker than the fields we are familiar with on Earth – can bind stars into galaxies. That’s all.

Good night.

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