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
Are you talking about astrology or astronomy? I admit that I’m not in the know about exactly how astrology is supposed to work but I don’t think it usually takes cosmic distances into account.
The distance to a star isn’t measured in “years,” so the question is confusing. In addition, you would need to specify whether the distance between your location and the star’s position is X at the time you leave, or whether the total distance you eventually travel would be X. Your location, and that of any other star, are constantly changing in relation to one another. Thus, there will not be a fixed distance between your position and that of any other star in the sky over any notable period of time.
The distance is measured in light years, so light travels at really huge speeds and so over vast distances between the stars it takes years for light to go from one star to another. 1 light year equals 9.46 trillion kilometres.
I suspect they wrote the question wrong or you miscopied, but I’m going to assume the star is 415 *light*-years away.
Light goes 300,000 kilometers per second, so it goes about 300,000 x 60 x 60 x 24 x 365 = 9.46×10^(12) kilometers per year, so it’ll go 415 times that far in 415 years: 3.93×10^(15) kilometers. Just under 4 quadrillion kilometers.
Divide that number by 99,700 and you get 3.94×10^(10) hours.
Divide that number by 24 and you get days: 1 billion, 641 million days.
Divide that by 365 and you get years: roughly 4.5 million years.
(The speed of light is actually a smidge under 300,000km/sec, and years aren’t exactly 365 days, so if you used more precise numbers in those places you’d get a better answer than mine.)
(I assume you’re in an astronomy course? Astrology is the “don’t take any risks this week because Jupiter is in Pisces” thing. Number crunch like this seems more like astronomy.)
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.
You seem to be mixing up a lot of words that don’t mean what you think they do.
Astrology is telling the future by looking at the planets and stars.
Astronomy is the science of studying stars (and everything else beyond earth’s atmosphere).
Cosmological usually mean really big scale stuff like studying the universe itself or the big bang or similar. 415 years or 415 light years would be far too small scale to qualify normally for that label.
You say that you want to go to a star that is 415 years away. Years measure time not distance. You probably mean light years.
If you want to know how long it takes to get some place and know the speed you are going and the distance it is at you can just divide the two.
A light year is defined to be exactly 9,460,730,472,580.8 km. we can multiply that by 415 and divide that by the 99700 km/h you asked about and get a number in hours that we only need to convert into years based on the number of hours in a year.
In this case that works out to be about 4.5 million years.
If you were going faster we would need to bring relativity into the math, but the speed you are suggesting while insanely fast is still less than one ten-thousands of the speed of light, so we need not bother.
Astrology: woo-woo fortunetelling.
Astronomy: science about observable universe.
Q: 415 years away traveling at 99700 kmh how many years does it take you
A: Its takes 415 years, that is the first thing in the problem that you state.
Take a moment, carefully read through your textbook what the problem you need to solve really is, think about it for a minute and then try again.
I assume that this question is about relativistic time dilation. So I assume the question means that at velocity v you will reach the object in 415 years in Earth’s frame of reference and so how long does this journey take in your frame travelling at v.
Well with a light clock (two mirrors and a beam of light) and a bit of Pythagoras you can derive that in the moving frame (relative to the reference/clock frame) elapsed time just gets gamma factored. So t’ (elapsed time in the reference coordinate system aka Earth I assume) is just t (the moving frame aka you) times the gamma factor 1/[(1-v²/c²)^(½)]. So t’=t×gamma or 415/gamma = t.
But I’m either missing something since with this velocity the gamma factor is practically 1, 99700 km/h isn’t fast enough for special relativity to be a major factor here.
Maybe the question states that the star is 415 light years away and in that case 1 light year = c×1 year = x km distance 415 × x km / km/h = t h amount of time.
See the others, but also:
You’re not travelling at 99700 km *times* h, but at 99700 km *per* h. (kph or km/s)
Also, “cosmic distances”, not “cosmological”. Distances on the scale of the cosmos, not distances on the scale of the study of the cosmos.
I think your issue was that you didn’t recognise that “lightyear” is a shortcut for the rather unwieldy value of 9,460,730,472,580.8 km. The distance light in a vacuum travels in one year. (BTW: You also may stumble upon the parsec later. That’s 30,856,775,714,409.19 km. Another simple shortcut.)
There’s nothing special about the lightyear other than that it incorporates the speed of light. But the other part, the length of an Earth year, is pretty arbitrary. The only reason such a random shortcut unit stuck around is that it’s better than having to measure those distances in metres…
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PS: And the answer naturally is “none at all because I wouldn’t agree to go on such a long journey.” 😉 😉 😉
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