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Orbital Radii of planets and moons of jupiter 
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#1
Feb307, 07:53 PM

P: 149

1. The problem statement, all variables and given/known data
Finally, develop models for only the four innermost planets and the four Galilean moons by reducing all the orbital radii by a factor that makes the orbital radius of the first planet or moon equal to one. Give possible reasons for the similarities and/or differences in two models. 2. Relevant equations x = position of planets relative to sun y = orbital radii Mercury Venus Earth Mars Asteriod Jupiter Saturn Uranus Neptune Pluto x 1 2 3 4 5 6 7 8 9 10 y 57.9 108.2 149.6 227.9 T 778.3 1249 2871 4504 5914 x = position of galilean moons relative to jupiter y = orbital radii Lo Europa Ganymede Callisto X 5 6 7 8 Y 422 670.9 1070 1883 3. The attempt at a solution This math portfolio asks us to find an equation relating x and y. I find this by plotting the points, and the best fit line. The equation is exponential. I solve for T (the orbital raidus of asteriod), T = 469 millions of kilometers. For this last question, I don't understand what they mean by the four "innermost" planets...And finding a factor (a common factor?).... The model for case A is: 1.19x^3.71 The model for case B is: 1.18^3.54 Also, is there another way, other than the graphical method, to find the equation relating x and y?? 


#2
Feb507, 05:50 AM

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#3
Feb607, 05:58 PM

P: 149

Thank you hallsofivy. I have one question, though. (Refering to your method)Do I use values from the given data to find the best fit line? For example,
log422 = b logx + logA. Then ? I do mention T (asteroid) in the table above. When I copy pasted the table off word, the grids disappeared, thus making it hard to follow. It's in sequential order...you just have to correspond the first x value to the y value in the second row...sorry for the misunderstanding. 


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Feb707, 05:14 AM

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Orbital Radii of planets and moons of jupiter



#5
Feb1207, 01:37 PM

P: 149

I have been researching your 'least squares methods" but I'm still struggling to apply it to my set of data! Help highly appreciated! Thank you!



#6
Feb1307, 09:15 PM

P: 2

You should consider doing your IB Type II Assessment on your own.



#7
Feb1407, 09:42 PM

P: 149

I wish to clarify a few things: I did do my Type II assessment on my own. Additionally, HallsOfIvy simply verified my work. S/he didn't, in any way, give away answers. And just for the record, I did not determine the equation algebraically until the day before yesterday when I came upon a method to do so as I was researching for a chemistryrelated topic.
Thank you, however, for your concern. 


#8
Feb1507, 07:06 AM

P: 2

The least squares method is basically finding the line of best fit (the square of the errors form the smaller number, therefore least squares). If you have a TI graphing calculator, you do linear regression.
You can do what hallsofivy did and enter in the data using logs and still use linear regression. What you do to find y at the end is raise the other side to a power of the base. However, that's the long way to get the equation. The simpler way is simply find exponential regression using the calculator. By the way, I thought this assessment was completely pointless. Aren't we trying to find a relationship that doesn't exist? 


#9
Feb1507, 08:24 AM

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