Solar Gravitational lens: Seeing alien planets

Solar Gravitational lens: Seeing alien planets

Let’s say in the future we pick up a signal from Proxima Centauri b – an exoplanet which is orbiting the star Proxima Centauri around 4.2 light years away.  It would be nice to jump in a spaceship to explore further – but even travelling at 61,500km/h (the speed of Voyager 1) this would take a depressingly long 74,000 years.  So, would the mysteries of the planet be forever out of reach?  Surprisingly not – thanks to a property of light which would allow us to harness the Sun to create an enormous lens which would be able to resolve the planet into incredible detail.

Using the Sun’s gravitational field

Say we have an exoplanet at point A which we wish to aim our telescope at – we can use the Sun as a giant lens to magnify this planet.  This works because the gravitational pull of the Sun will bend light waves travelling from point A.  If we position the telescope in exactly the right location (C), then the Sun will act like a giant lens, focusing these light waves onto the telescope. 

In the diagram above, the yellow circle represents the Sun and the larger grey circle represents the gravitational field.  A light wave travelling from A travels in a straight line until hitting the gravitational field of the Sun and is then bent towards C.

We can define d as the distance from the exoplanet and the centre of the Sun, r as the distance from the centre of the Sun to the rays, and F as the distance from the centre of the Sun to the telescope.

Where to position the telescope?

We can simplify things by setting the focus such that the rays of light just touch the edge of the Sun.  This then gives r as the radius of the Sun.

We can now use the following formula to find where to place the telescope:

We need to keep a consistency of units.  The gravitational constant G has the following value and units:

So we need all our other measurements to be in kg, metres and m/s.  This gives:

We can then calculate the distance away from the Sun that the telescope needs to be in km:

 

And put this in context by calculating it in AU (1 astronomical unit (AU) is the average distance from the Sun to the Earth).

So, for rays just touching the edge of the Sun – the telescope should be placed at a distance of 550 AU (550 times the distance from the Earth to the Sun).  This is still a large technical challenge but would be achievable using current technology (given sufficient budget).

How great a magnification could we achieve?

We can determine how large the image of the exoplanet would be using this method by using the following formula:

For the case of Proxima Centauri b we would have:

This then gives:

Now at first glance this presents another clear problem – we would need a focal plane 30.5km by 30.5km to receive the image!  Luckily there is another clever trick involving the properties of Einstein rings to resolve this – so processing this information is also technologically possible.

What would this look like?

The scale factor of this image is given by 14900/30.5, which gives around a 1:500 scale. This is an incredible level of detail.  This means that every 5 metres of the surface would be represented by 1cm on our projection.  At this level of detail you would be able to see surface details (assuming no cloud cover etc.) down to the level of individual buildings.  You can see a Google Earth zoom to the scale of 1:500 on Big Ben in London below:

Now, in reality it may not be able to resolve detail to such a level – but astronomers believe that this technique would indeed have the ability to make out structures and other tell-tale signs of civilization.  Indeed they have calculated that this technique is so powerful, that if a 1 watt laser was shone in the direction of the Sun from Proxima Centauri b, that this would be picked up by the telescope.

Incredible stuff – and who knows, maybe a similar telescope is pointed at Earth right now!