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March 1st, 2013, 12:33 PM   #1
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a very confusing problem in my math book

Earth moves in a roughly circular orbit around the at a distance of approximately 150 000 000 km. To estimate long distances in space, scientists measure in multiples of the Earth-sun radius or astronomical units
(1 AU = 149 597 870.691 km). NASA defines 1 AU as the radius of an unperturbed circular orbit of a massless theoretical body revolving about the sun in days, where k is a constant exactly equal to 0.017202098.95.

(a) Placing the sun at the origin, write an equation representing Earth's orbit (in AU), assuming a circular orbit.

(b) One year on Mars represents one complete rotation. How long (in radius) is 1 Mars-year on Earth. How long is this in Earth days? The orbital radius of Mars is roughly 1.5 AU.

my solution
(a) Because Earth moves around the sun in a roughly circular orbit, I use the equation of a circle centred at the origin. Since the distance from the sun to the Earth is approximately 1 AU, I write

I am completely stuck in part (b).

Please help me. Thanks.
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March 1st, 2013, 12:51 PM   #2
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Re: a very confusing problem in my math book

For part b), I would use Kepler's third law of of planetary motion and state:



Thus, using the given assumptions, a year on Mars is about 1.84 Earth years.

This is close to the true value which is closer to 1.88 Earth years.
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March 1st, 2013, 01:27 PM   #3
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Re: a very confusing problem in my math book

[quote="MarkFL"]For part b), I would use Kepler's third law of of planetary motion and state:

I got this problem in a high school Math book not in a Physics book. Nowhere in my math book mentions Kepler's third law of planetary motion.

Is there another way to tackle this problem?
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March 1st, 2013, 01:54 PM   #4
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Re: a very confusing problem in my math book

I don't see how; we need to know how the radius and period are related. Kepler's third law of planetary motion provides this relationship.

Have you given the problem exactly as it appears in the book? I found this part:

"How long (in radius) is 1 Mars-year on Earth"

to be confusing, as it seems we are being asked how long a year on Mars is relative to an Earth year, but this would be in units of time, not of length.
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March 1st, 2013, 10:00 PM   #5
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Re: a very confusing problem in my math book

Quote:
Originally Posted by MarkFL
I don't see how; we need to know how the radius and period are related. Kepler's third law of planetary motion provides this relationship.

Have you given the problem exactly as it appears in the book? I found this part:

"How long (in radius) is 1 Mars-year on Earth"

to be confusing, as it seems we are being asked how long a year on Mars is relative to an Earth year, but this would be in units of time, not of length.
I was trying to help my friend's brother on this problem. He showed me a handout of math problems from his math teacher.
He said that his teacher got all the problems in a math book.
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