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

Question

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

Answer 1

I need to know if this makes sense of not and why?

Answer 2

7*7 = 49 which is about 50

Answer 3

Yes, it makes sense, 7 times further is 1/49 th of brightness

Answer 4

To show that the Hubble Space Telescope can see about seven times farther than a ground-based telescope, we can use the inverse square law of brightness.

The inverse square law states that the intensity (or brightness) of a point source, such as a star, decreases as the square of the distance from the observer increases. Mathematically, this can be expressed as:

I ∝ 1/d^2

Where I is the intensity (brightness) of the object and d is the distance from the observer.

Now, let's compare the brightness of a star as observed by the Hubble Space Telescope and a ground-based telescope.

Let's assume that the brightness of the faintest object observable by a ground-based telescope is 'I_ground' and the distance between the object and the observer is 'd_ground'. Therefore, we can write:

I_ground ∝ 1/d_ground^2

Similarly, let's assume that the brightness of the same object observed by the Hubble Space Telescope is 'I_hubble' and the distance between the object and the observer is 'd_hubble'. Therefore, we can write:

I_hubble ∝ 1/d_hubble^2

According to the given information, the Hubble Space Telescope can see stars and galaxies where the brightness is 1/50 (or 1/50 times) of the faintest objects observable using ground-based telescopes. We can express this relationship as:

I_hubble = (1/50) * I_ground

Now, let's substitute the above expressions into the equation:

(1/50) * I_ground = 1/d_hubble^2

Simplifying the equation, we can rearrange it to solve for d_hubble:

d_hubble = √(50 * d_ground^2)

d_hubble = 5 * √(d_ground^2)

So, the distance at which the Hubble Space Telescope can observe an object is approximately 5 times the distance at which a ground-based telescope can observe the same object.

Therefore, the Hubble Space Telescope can see about seven times farther (5 times farther compared to a ground-based telescope) based on the inverse square law.