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Ashok Kumar, Electrical Engineer
Category: Math Homework
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Experience:  Master's Degree
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# Velocity is the distance traveled divided by the time taken.

### Customer Question

Velocity is the distance traveled divided by the time taken.
In Carl Sagan's Cosmos Part 8 about 33 minutes in he says,
"We could travel to the Andromeda Galaxy in 28 years ship time."
The Andromeda Galaxy is approximately 2.5 million lightyears away.
2.5e6 lightyears / 28 years = 89,285 light years per year
If a lightyear is a distance and a year is a measure of time,
How is it they are traveling almost 90,000 times the speed of light?
Submitted: 8 months ago.
Category: Math Homework
Expert:  Ashok Kumar replied 8 months ago.

I will go through it. Kindly inform when it is due.

Customer: replied 8 months ago.
Expert:  Ashok Kumar replied 8 months ago.

thanks. I am trying it.

Expert:  Ashok Kumar replied 8 months ago.

We will have to consider galaxy travels.

we have t =(2c/g)ln(gD/c^2)

where t = time

c = light velocity = 3*10*8 m/sec

g = 9.8m/sec

D = distance in meters

1 lightyear = 9.53*10^15 metes and 1 year = 3.153 *10^7 secs

We will determine time using these values.

Here D = 2.5*10^6 light years = 2.5*10^6*9.53*10^15 m

Putting these values, we get

t = (2*3*10^8/9.8)ln(9.8* 2.5*10^6*9.53*10^15/9*10^16)

=###-##-####2 secs

=###-##-####2/3.153*10^7

= 28. 67 years

This is same time as given in problem.

the attached referred file has been taken from the following link:

Customer: replied 8 months ago.
I went over the numbers as you outlined and it checks out but you have not answered my question...
"How is it they are traveling almost 90,000 times the speed of light?"
When the speed of light cannot be broken?
Expert:  Ashok Kumar replied 8 months ago.

I calculated time taken to travel considering light velocity as 3*10^8m/sec.

Alternatively, we can put time and find the light velocity and it will be about 3*10^8m/sec.

This way yr query is replied.

Customer: replied 8 months ago.
Again I am not arguing with the math, just the philosophy that from the ship's point of view when they are at the mid point they observe Andromeda apparently approaching at many times the speed of light. The distance between the end points has not changed significantly (2.5e6 light years). 28 years is significantly less then the speed of light distance. The conclusion is that the speed of light is relativie to the observer. In other words there is a velocity bubble that follows the observer. As the observer accelerates the bubble leaves objects behind and gains new objects ahead. In this way relativity makes sense. It is possible to travel faster than the speed of light but you are not in the same universe when you do.
Expert:  Ashok Kumar replied 8 months ago.

I can not comment on this but yr doubt has been clarified.

Customer: replied 8 months ago.
Part of my process is to Q & A. It seems I am unable to see through to the solution unless I have a sounding board.
I am 100% Satisfied. Thank you Kumar for your participation.
Expert:  Ashok Kumar replied 8 months ago.

can u rate it?