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Circular orbits

  1. Mar 9, 2005 #1
    i was hoping somebody could give me a hand with a homework problem i have .

    first here's the question .

    -> Planet X has two satellites . A and B . Both orbits are circular . Satellite A's orbital radius is 4 times B's orbital radius . calculate the following ratios .

    a) A's orbital period / B's orbital period
    b) A's orbital speed / B's orbital speed


    -----


    now i'm kind of stumped because of the lack of information .
    for a) i know that the ratio of orbital periods is the ratio of the T's . but i'm absolutly losing it trying to figure out how to find the T's .
    i know that ((4pi^2)/G) (R^3/T^2) ) = M1 + M2
    and R^3 = T^2 , also C = 2piR . but i can't for the life of me see how i could get the desired ratio with those formulas . does anybody know if i'm on the right track ? or should i be using some other formula that i'm somehoe missing ?
     
  2. jcsd
  3. Mar 9, 2005 #2

    BobG

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    Science Advisor
    Homework Helper

    a) Kepler's third law says what. It explains the relationship between the radius and the orbital period. In other words, the relationship is explained by 2 key variables: T^2 and r^3. Everything else could be replaced by a single constant

    b) Same reasoning. What's the relationship between speed and the radius. If the radius increases by a certain amount, does the speed increase or decrease? By how much?

    Technically, you could let orbit B have a radius of '1' and orbit A have a radius of '4'. Then you could plug each into the appropriate equation, plug your answer into your ratio, and simplify. It's just easier to combine all of the constants into one called c, since the same constants will appear in both the numerator and the denominator and will cancel out.

    Actually, the equation for each is:

    [tex]\tau^2=\frac{4 \pi^2 r^3}{\mu}[/tex] with mu being the geocentric gravitational constant.

    [tex]S = \frac{\sqrt{\mu}}{\sqrt{r}}[/tex]
     
    Last edited: Mar 9, 2005
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