Solving Another Kibble Problem - Homework Statement & Equations

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In summary, the author solved for the difference in times by dividing the area of the ellipse that the position vector sweeps out every year by pi*a*b/year.
  • #1
haplo
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Hi everybody, thank for helping with previous problem. I have another quesion:
This is not an actual problem. While the problem is actually solved in the book one of the steps there is not entierly clear as a result I cannot understand simmilar problem.
So here it is

Homework Statement


IF the Earth orbit is divided into by it's minor axis, how much does it spent in one half than another.

Homework Equations



Here is how is is solved in text. Eccentricity of Earth orbit is 0.0167. It is clear that area of swept are is 1/2 area of elipse plus/minus the area of triangle with base 2*b and height ae. so A=1/2*Pi*a*b plus/minus a*e*b. Thus the time tame n are (1/2 plus/minus e/Pi) Years.

Thats what I have difficult understanding. How did they make a jump from area to years. Apparently the second evauation was obtined by dividing A over area of elipse a*b*Pi. If this is the case, how did author extracted years?
 
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  • #2
The text used Kepler's second law. Is that the question?
 
  • #3
It was one of my guesses. If the second keplers law is used than dt=constant/da= J/(2*m*da) . I just fail to see why suddenly Pi appears in the denominator, as if they divided area by a*b*Pi
 
  • #4
The ratio of the areas swept is proportional to the ratio of the times. I've got to say I'm having problems following the rest of your post. But the ratio of the areas of the triangles is also proportional to the areas of the corresponding parts of the ellipse.
 
  • #5
Hi there again,

I really struggled to figure out how they got the final answer for the difference between the times in this example.

But here's how I eventually got the answer (using what Dick suggested you use in his reply above):

The position vector sweeps out a total area of pi*a*b every year (period of the Earth's orbit around the sun). So if you divide 0.5*pi*a*b +/- a*e*b by pi*a*b / year, it will give you the final answer 0.5 +/- e/pi years, the difference between the times spent by the position vector in the two halves of the Earth's orbit.

Hope this helps,

Wynand.
 
  • #6
thakns!, it is just Pi*a*b/year, dam I am retarded..
 
  • #7
Don't mention it, I'm glad I could be of help:)

I don't think you're a retard, otherwise I'm one too:

I was actually completely bewildered when I first read this example. I didn't even realize that the origin of the position vector was one of the foci of the ellipse. I was still thinking in terms of the centre of a "circle". Haha - how's that for forgetting high school analytic geometry?
 

1. What is the purpose of this homework problem?

The purpose of this homework problem is to practice solving a real-world scientific problem using equations and mathematical reasoning. It also helps to develop critical thinking skills and problem-solving abilities.

2. Can you provide an explanation of the given equations?

Yes, the given equations in this homework problem represent the relationship between the amount of kibble needed for a certain number of cats and the cost of the kibble. The first equation calculates the total amount of kibble needed based on the number of cats and the average daily amount of kibble per cat. The second equation calculates the total cost of the kibble based on the price per pound and the total amount of kibble needed.

3. Are there any assumptions made in this problem?

Yes, this problem assumes that all cats will eat the same amount of kibble per day and that the price of kibble per pound remains constant.

4. How can this problem be solved?

This problem can be solved by setting up and solving the given equations using algebraic manipulation. The solution will provide the specific amount of kibble needed and the total cost of the kibble.

5. How can this problem be applied to real-life situations?

This problem can be applied to real-life situations by using the same problem-solving process to determine the cost of other supplies or services based on different variables such as quantity and price. It also highlights the importance of considering multiple factors and using mathematical reasoning to make informed decisions.

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