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Math Help - confused about tangents

  1. #1
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    confused about tangents

    I'm o.k. at algebra, but have an equation to solve that involves a tangent, and the concept is not clear to me. Here is the equation...(it's about determining the mass of two objects by how the path of one object is changed as it comes close to the other object)

    tan 1/2 (theta) = G(m=M)/(v)2 b where,

    theta = angle of deflection
    M and m are the masses of the two objects in question
    G is the gravitational constant
    v is the relative velocity of the encounter
    b is the impact parameter

    I'm confused about the "tan" part. Since theta is an angle, in this case 0.05 degrees, what is it that I'm supposed to use the tanger of? Is this simply a matter of looking up the tangent of 1/2 times (0.05)?

    If this question would best be posted elsewhere, please let me know.

    Thanks in advance!

    John
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  2. #2
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    Quote Originally Posted by heartland55 View Post
    I'm o.k. at algebra, but have an equation to solve that involves a tangent, and the concept is not clear to me. Here is the equation...(it's about determining the mass of two objects by how the path of one object is changed as it comes close to the other object)

    tan 1/2 (theta) = G(m=M)/(v)2 b where,

    theta = angle of deflection
    M and m are the masses of the two objects in question
    G is the gravitational constant
    v is the relative velocity of the encounter
    b is the impact parameter

    I'm confused about the "tan" part. Since theta is an angle, in this case 0.05 degrees, what is it that I'm supposed to use the tanger of? Is this simply a matter of looking up the tangent of 1/2 times (0.05)?

    If this question would best be posted elsewhere, please let me know.

    Thanks in advance!

    John
    Hi John,

    Maybe someone will be familiar with that equation, but I find it illegible. How can you have a second equation m=M within the overall equation? In addition to other issues. Consider reading the LaTeX Tutorial in the LaTeX Help subforum. Otherwise, consider being very careful about parentheses and the like.
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  3. #3
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    How close is this?

    \displaystyle \tan\left(\frac{\theta}{2}\right)=\frac{G(m+M)}{v^  2b}
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    Actually, the equation should look like this (I just didn't type it correctly)..

    tan 1/2 (theta) = G(m+M)/(v)2 b where

    The idea is to get the total mass of a system, so I could rewrite the equation this way...

    tan 1/2 (theta) =GM/(v)2 b

    Plugging all the numbers in, it looks like this...

    tan 1/2 (0.05) = 66700000 (M)/4000

    and simplyfying it looks like this (I think)...

    M = tan 1/2 (0.05)(4000)/6670000000

    My question is I'm not sure where I'm supposed to get the value for "tan" from.

    Thanks!

    John
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  5. #5
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    Ha! Basically, that's it. The question that is still not clear in my mind is where I get the value for "tan". Do I just take theta (in this case its 0.05 degrees), divide it by 2, then pull the tangent out of a table?

    Thanks again!

    John
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  6. #6
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    Quote Originally Posted by heartland55 View Post
    Ha! Basically, that's it. The question that is still not clear in my mind is where I get the value for "tan". Do I just take theta (in this case its 0.05 degrees), divide it by 2, then pull the tangent out of a table?

    Thanks again!

    John
    What do you mean by "basically"?

    \tan(0.025^\circ)\approx 0.000436332. Does this help?
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  7. #7
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    Yes, that does help. So by plugging in the numbers it comes out that (M + m), the total mass of the two bodies = 26166857 kg.

    One of these bodies is 50km in diameter, and the other is 250km. Does is follow that the smaller body (assuming that the density of each body is the same, and that both are spheres) is 1/5 the mass of the larger, i.e. 5233371 kilograms?
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  8. #8
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    Quote Originally Posted by heartland55 View Post
    Yes, that does help. So by plugging in the numbers it comes out that (M + m), the total mass of the two bodies = 26166857 kg.

    One of these bodies is 50km in diameter, and the other is 250km. Does is follow that the smaller body (assuming that the density of each body is the same, and that both are spheres) is 1/5 the mass of the larger, i.e. 5233371 kilograms?
    No, volume of a sphere is proportional to radius cubed. So the smaller body has 1/125 the mass of the larger, with the assumptions you mentioned. By the way if you assume 1/5 then 5233371 still isn't right because you need to divide 26166857 by 6 in order to get 1 part small body to 5 parts large body.
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  9. #9
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    Whoops! Good point. So the larger body is about 2.59x10^7 kilograms, and the smaller about 2.08x10^5 kilograms (getting that from dividing the total mass by 126, then multiplying by 125 for the larger body mass).

    This will be fun once the rust comes off!
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