Growing Faster than

the Speed of Light?

 

Using Pythagoras’ Theorem to Find Difference between Actual Growth & Apparent Growth

 

Part 2

 

 

 

 

 

      

 

B                                              C                                              D                                              E

 

For each of the images above we are aiming to find the difference between the lengths of each red line, the apparent growth, and each blue line, the actual growth.

 

We will use, essentially, the same procedure as we did in image A but with an extra twist to find the lengths of the red lines.

Remember that in the images the letter ‘x’ refers to the unknown distance of the whole of the left hand side of the triangles and the letter ‘y’ refers to the unknown distance of each red line.

 

For image B:

 

We have a right-angled triangle with sides of 3, 5 and ‘x’.

 

We can find the side length ‘x’ by doing:

 

 

(in light-months)

 

We now need to use this to find the length of the red line only, the apparent growth, or ‘y’.  To do this we need to know the length of the green bit and then subtract this from ‘x’ (or 4 as we have found out).

 

Luckily, we know the length of the green bit from our calculations of image A – it was 2.65 – so:

 

 

This is the length of the red line, the ‘apparent growth’.

To find the difference between this and the ‘actual growth’ (the blue line, which is 1 light-month), we subtract the ‘actual growth’:

 

 

So the difference in apparent growth and actual growth after 3+1, or 4, months is 0.35 light-months.

 

For images C, D and E the process above is repeated using figures from the previous image each time

(ie for image C use Left hand edge of image B, for image D use left hand edge of image C etc).

 

 

 

 To check your answers click here.