Hubble Telescope

Why don't we just point Hubble or some other big telescope at the moon to show the moon landing sites?  Wouldn't that settle the argument once and for all?

If only it was that easy!  The biggest problem with this is that they simply are not powerful enough.  The lunar landers are very,very,very small in astronomical terms and they're pretty far away as well.  There isn't a telescope in existence that could take a picture of one.

There are lots of mathematics we could show to demonstrate this, but's it's very complicated and we don't fully understand it anyway.  But here's our abridged dumbed-down version.

Size of Lunar Module.   Let's be really generous and say 10m square.

Distance between Hubble and Moon.  About 350, 000km.

This works out as an visual angle of     (10m)/(3.5 x 10^8m) * (180/PI) = 1.6 x 10^-6 degrees = 6 milliarcseconds.

The WFPC2 'telescope' on Hubble has the following resolution:   800x800 pixels of a 35 arcseconds field of view with a pixel scale of 46 milliarcseconds.   Actually resolution in practice is a little below this.

So what does this all mean?  Well, roughly speaking, it means that the lunar lander would have to be 15 times larger before it would even cause a dot on a Hubble picture.

(We have to thank Terry Hancock for helping us out with this info.   You didn't think we worked it out ourselves, did you?   If there's any errors in it, they almost certainly lie with our interpretation of his explanation.)

or, to look at it another way....

We stole the following off a NASA discussion board.  We would usually just link to it, but discussion messages have a habit of expiring and this was too good to lose.    Ed Cheng explains there's a law of physics that would prevent Hubble seeing the Lunar Module, and it's to do with the size of its light collecting mirror.  

The wavelength of visible light is around 550x10^-9m  (i.e. very very small).

The diameter of Hubble's mirror is 2.4m.

Highest ever physically possible resolution  = 1.4 x 550 x 10^-9 /2.4 m = 3.2 x 10^-7 radians

At a distance of 350,000km this works out as about 124 metres.    As Ed says, roughly the size of a football field.

So even if Hubble's camera had a greater resolution, it still couldn't see the Lunar Module.

But doesn't this same Hubble take photos of things billions of light years away?   Yup. 

Makes you feel very very very small, doesn't it?