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Math Help - planet motion

  1. #1
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    Exclamation planet motion

    I have this q, its long to explain but iv dont the first parts just need help with the last 2 q's

    The planet saturn has many moons.The table below gives the mean radius of orbit and the time taken to coplete one orbit for five of the best known of them.
    See the table .
    It is believed that the relationship between R and T if of the form R=kT^n.
    i) how can this be tested by plotting log T against log R? which iv done and drawn the graph.
    ii)make out a table of values of log R and log T and draw the graph. Also done this.
    iii) But from my grap i need to estimate the values of k and n. (from my graph the gradient is 0.67 and the intercept it 0.275) I need help to Solve k and n.
    In 1980 a voyager spacecraft photographed several previously unknown moons of saturn. One of these named 1980 S.27 , has a mean orbital radius of 1.4 x10^5km.
    iv) Finally i need to estaimate how many days it takes this moon to orbit saturn. Which i need help with.



    thank you!
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  2. #2
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    Hello,

    iii) But from my grap i need to estimate the values of k and n. (from my graph the gradient is 0.67 and the intercept it 0.275) I need help to Solve k and n.
    Well, this is not very difficult if you see the thing

    R=kT^n

    So log(R)=log(k)+n*log(T)

    I'm not sure whether you have log(R) in the ordinates. Nevermind...If it's not this way, express log(T) in terms of log(R).


    In a function y=ax+b, a is the gradient and b the intercept.
    So can you conclude ?
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  3. #3
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    In 1980 a voyager spacecraft photographed several previously unknown moons of saturn. One of these named 1980 S.27 , has a mean orbital radius of 1.4 x10^5km.
    iv) Finally i need to estaimate how many days it takes this moon to orbit saturn. Which i need help with.
    So R=1.4 (since your graph is x10^5 km)

    Plug it in log(R)=log(k)+n*log(T)

    So you'll have something like log(1.4)="intercept"+"gradient"*log(T)

    -> log(T)=(log(1.4)-"intercept")/"gradient"

    ---> T=exponential of all the thing
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  4. #4
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    hi, i dont understand that..it says use the graph... :S thanks

    For the second one what isT, iv put into my calc, (log(1.4)-0.275)/0.67 and got -0.192 , i that because i dont now T?
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  5. #5
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    Hm, so calculate log(1.4), find the ordinate of the point which has log(1.4) as absciss and you'll have log(T) )
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    iv done the second question..lol by doing a better graph...then just seen your post lol..so now i just need to find the values of k and n, i should be able to do this by using the graph...but i cant see a way..iv tried log the gradient and intersection values, but i just gt negatives ...
    Thank you..you are being a big help

    Y do you want to beat janvl?
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  7. #7
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    So if you've graphed a better thing, find the gradient of the line and the intercept.

    As I've told you, since R=kT^n, log(R)=log(k)+n*log(T) (properties of logarithm).
    And this function is the one represented by the graph as you took log(R) and log(T).

    Hence the gradient of the line you got is n, according to the formula and the intercept will be log(k).

    If you have for example "b" for the intercept, then log(k)=b and k=e^b



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