How do telescopes allow us to see light sources millions of light years away?

[Clay]

i have heard how our broadcasts will be seen by aliens far away or whatever.
but i realize those signals are going to "attenuate" by d^-2

anyway...
how come in astronomy we can see light sources millions of light years away? shouldn't those signals be far too weak to detect after such a long distance?furthermore i am confused about the concepts of "power" and "intensity"

say we have a 100kw isotropic radio antenna
so at, say, 5 meters away, what is our power? what is our intensity? (assume vacuum)

 

[Dale]

how come in astronomy we can see light sources millions of light years away? shouldn't those signals be far too weak to detect after such a long distance?

They start off as really really big signals.

 

[FactChecker]

Power is energy per unit time. Intensity is power per unit area (where the area is measured perpendicular to the direction the light is coming from).

 

[Janus]

i have heard how our broadcasts will be seen by aliens far away or whatever.
but i realize those signals are going to "attenuate" by d^-2

anyway...
how come in astronomy we can see light sources millions of light years away? shouldn't those signals be far too weak to detect after such a long distance?

1. We use telescopes with large apertures that can gather much more light than our eyes can.
2. We spend a lot of time gathering light from what our telescope is pointed at. The Hubble telescope can spend weeks looking at a single spot in the sky, slowly collecting light in order to build up an image.