modeling using variation Hubble telescope

Question

The Hubble Telescope can be used to see stars and galaxies whose brightness is about 1/50 of the faintest objects that now observable using ground-based telescopes.
• With the fact that the brightness of a point source, such as a star, varies inversely as the square of its distance from the observe, show that the Hubble Telescope can see about seven times farther than a ground-based telescope.

Answer 1

Assume the ground telescope sees an object of brightness 1 at a distance d, and assume the Hubble sees the same object at a brightness of 1/50 at a distance ad.  You know that brightness is inversely proportional to the square of the distance, so the product of brightness and distance squared is the same for both telecopes.

 

(1)d² = (1/50)(ad)²

 

Solve for a. 

 

a² = 50

 

a = √50 ≅ 7.071 ≅ 7

 

Hubble can see the same object 7 times farther away than what the ground telescope can see.