If we can use it to see farther than we have ever seen before why haven’t they got a really good close up of the nearest Solar system outside of our own?
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There’s 2 things that affect what you can make out with a telescope just by the nature of optics. The size of the telescope D, and the wavelength of light you are using λ. These limit how far apart in your field of view you can differentiate 2 objects θ (which is an angular measurement in radians). For reference, the full moon takes up about half a degree of space in the night sky.
A better way to explain θ would be tan(θ)=size of target/distance to target. Since we are working with very small angles, we can approximate that to be θ=size/distance
The formula is sin(θ)=1.22λ/D and again for very small angles we can approximate θ=1.22λ/D
A small θ means a high resolution. The 1.22 is when the first rings of “blurriness” start. See the double slit experiment as to why that happens.
This means that for larger λ (longer wavelengths) θ gets larger. For larger D (larger telescopes) θ gets smaller.
We can’t control how far away things are or what kind of light they emit, so we are very limited in the kind of objects we can see.
For example, let’s say Jupiter is orbiting Proxima Centauri, 4.24 ly away. In order to be able to visually tell it is separate from the star, we would need a telescope about 40m across (ignoring the fact that the star would drown out any light coming from Jupiter). In order to actually be able to see the planet in isolation we would need one 430m across. (Keep in mind this is for visible light and I did a lot of rounding)
Another problem is wavelength. The JWST is designed to look into deep space, but since space is constantly expanding, that means the light from distant objects is redshifted. This means it has a longer wavelength than when it was created, so the JWST is designed to pick up those longer wavelengths, which aren’t useful for observing nearby stars which are in visible light ranges.
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