Question

Listed following are several fictitious stars with their luminosities given in terms of the Sun's luminosity (LSun) and their distances from Earth given in light-years (ly). Rank the stars based on how bright each would appear in the sky as seen from Earth, from brightest to dimmest. If two (or more) stars have the same brightness in the sky, show this equality by dragging one star on top of the other(s)

Enzo: 200 LSun , 20 ly Ferdinand: 400 LSun , 20 ly Nismo: 100 LSun , 8 ly
Lotus: 400 LSun , 40 ly Shelby: 100 LSun , 10 ly

Answer 1

1. Nismo:
`L_(a)=0.1244`

2. Ferdinand:
`L_(a)=0.0796`, Shelby:
`L_(a)=0.0796`

3. Enzo:
`L_(a)=0.0398`

4. Lotus:
`L_(a)=0.0199`

Step-by-step explanation:

The luminosity of a star is the amount of light it emits from its surface. The luminosity is an intrinsic property of the star. Apparent brightness is how bright the star appears to a detector on Earth. Apparent brightness is not an intrinsic property of the star; it depends on the location of the observer.

As light travels towards an observer, it spreads out and covers a larger area, reducing the intensity. Thus the apparent brightness is inversely proportionate to the square of the distance between the star and observer.

Apparent brightness can be calculated by the formula below:

`L_(a)=(L)/(4*pi*D^(2))`

Where,
`L_(a)` is apparent brightness,
`L` is luminosity,
`D` is the distance between the star and observer

Enzo: 200 LSun , 20 ly

`L_(a)=(L)/(4*pi*D^(2))`

`L_(a)=(200)/(4*pi*20^(2))`

`L_(a)=0.0398`

Ferdinand: 400 LSun , 20 ly

`L_(a)=(L)/(4*pi*D^(2))`

`L_(a)=(400)/(4*pi*20^(2))`

`L_(a)=0.0796`

Nismo: 100 LSun , 8 ly

`L_(a)=(L)/(4*pi*D^(2))`

`L_(a)=(100)/(4*pi*8^(2))`

`L_(a)=0.1244`

Lotus: 400 LSun , 40 ly

`L_(a)=(L)/(4*pi*D^(2))`

`L_(a)=(400)/(4*pi*40^(2))`

`L_(a)=0.0199`

Shelby: 100 LSun , 10 ly

`L_(a)=(L)/(4*pi*D^(2))`

`L_(a)=(100)/(4*pi*10^(2))`

`L_(a)=0.0796`

Apparent brightness of stars is summarized as below. Absolute values are considered as units are unspecified

Enzo:
`L_(a)=0.0398`

Ferdinand:
`L_(a)=0.0796`

Nismo:
`L_(a)=0.1244`

Lotus:
`L_(a)=0.0199`

Shelby:
`L_(a)=0.0796`

Organized in order of apparent brightness

1. Nismo:
`L_(a)=0.1244`

2. Ferdinand:
`L_(a)=0.0796`, Shelby:
`L_(a)=0.0796`

3. Enzo:
`L_(a)=0.0398`

4. Lotus:
`L_(a)=0.0199`