Physics Assessment #85 Transnational motion

[LuminousTruth]

How many centuries will be required for mercury's perihelion to precess 360 degrees?

A) (360/60) * (60*500)
B) (360) * (60/60) * (500)
C) (360) * (60) * (60/500)
D) 360 * 60 * 60 * 500

The answer is "C"

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I get how they used the eq d=(rate)*t where d is in theta and rate is in arsecs/cent.
t=d/rate
=> t= 360/[(500 arsecs/cent * (1 arcmin/60 arsecs) * (60 degree/1 arcmin)]
=> 360 / (500*(1/60)*60)

But I do not get how 1 min is 1/60 of a degree. It seems arbitrary to make 1 min ~ degree. Is it just standard usage/conversion? Can someone explain why that is the case?

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[rjosh33]

I don't know the answer to your question (I hadn't even heard of arcsec before this problem), but there's a different way to solve this problem that might be helpful in the future.

The question asks for an answer in centuries, and we're given a conversion factor of 500 arcsec/century. So, in order to get century in the numerator, the conversion factor must be inverted, putting the 500 in the denominator. Answer C is the only one that also has the 500 in the denominator, making it the right choice.

Of course, if another answer choice also had a 500 in the denominator this wouldn't work as well, but at least you would be able to use POE to narrow the answers down to 2, and then go from there.

 

[PhysMatMan]

Arcseconds and arcminutes are just units like feet or volts and therefore ultimately arbitrary. Their conversion however is consistent with our time measurements: 1 min=60 sec, 1 arcmin = 60 arcsec http://en.wikipedia.org/wiki/Arcsecond#Symbols_and_abbreviations

The problem should be solved with dimensional analysis.
We want centuries, so we have
[centuries] = [centuries/arcsec]*[arcsec/arcmin]*[arcmin/degrees]*[degrees]
->Answer= (1 century/500 arcsec)*(60 arcsec/arcmin)*(60 arcmin/degree)*(360 degrees)

 

[TheJourney]

What a question. The worse is when you read several explanations and still don't understand how they arrive to the correct answer.
I agree with OP, is it expected to know that an arc minute is equivalent to 1/60 of a degree.
I enjoyed rjosh33's explanation, I hate dimensional analysis.