I am in astrology and I have to calculate cosmological distances between things in space and I need help with the math
There is the question
you have to go to a star that is 415 years away traveling at 99700 kmh how many years does it take you
In: Mathematics
I assume you mean “415 light years”, not “years”. Otherwise, the answer is “415 years.”
The way we solve a question like this is with “dimensional analysis.” We’re given two values with dimensions/units that don’t match up (“light years” and “kilometers per hour”) and we’re supposed to bridge the gap to get answers in a third dimension/unit (“years”).
Start with the equation you need (rate = distance/time) and manipulate it to get the form you want (time = distance/rate).
T = (415 lightyears) / (99700 km/h).
Dividing by a fraction is the same as multiplying by its reciprocal.
T = (415 lightyears) * (1/99700 hours/kilometer)
Now, you can always multiply something in an equation by one, and the division of two equivalent things is one. So that means you can multiply the right side by (1 day / 24 hours) without changing it.
T = (415 lightyears) * (1/99700 hours/kilometer) * (1/24 days/hour) = (415 lightyears) * (1/2392800 days/kilometer).
And you keep repeating until the units are what you want.
T = (415 lightyears) * (1/2392800 days/kilometer) * (9.461 * 10^(12) kilometers / lightyear) * (1/365.25 years/day).
The lightyears in the numerator and denominator cancel out, and so do the kilometers, and so do the days. You get:
T = 415 * 1/2392800 * 9.461 * 10^(12) * 1/365.25 years.
Or about 4.5 million years.
There are cleverer ways to approach this specific problem, but this is the general way to handle many problems in math, physics, and astrophysics.
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