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Math Help - Angular measure problem help

  1. #1
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    Angular measure problem help

    I'm given the following diagram of a satellite orbiting above a planet.
    http://i.imgur.com/1BEQX.png

    I am then told to find the height of the satellite above the planet, but I don't really have any idea how to start solving this one. If someone could give me a push in the right direction that would be much appreciated.
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  2. #2
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    Quote Originally Posted by BobRoss View Post
    I'm given the following diagram of a satellite orbiting above a planet.
    http://i.imgur.com/1BEQX.png

    I am then told to find the height of the satellite above the planet, but I don't really have any idea how to start solving this one. If someone could give me a push in the right direction that would be much appreciated.
    familiar with the equation for arc length?

    s = R \cdot \theta

    note ...

    (1) \theta has to be in radians and

    (2) R is the distance from the center of the planet to the satellite.

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  3. #3
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    Quote Originally Posted by BobRoss View Post
    I'm given the following diagram of a satellite orbiting above a planet.
    http://i.imgur.com/1BEQX.png

    I am then told to find the height of the satellite above the planet, but I don't really have any idea how to start solving this one. If someone could give me a push in the right direction that would be much appreciated.
    You are given the arc length s = 8952 km and the angle it traces out. s = r \theta where r is the distance from the satellite to the center of the Earth. (The angle needs to be convert4d to radians first.)

    -Dan
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    So I convert 55 to radians which gives me 0.9599310886 and then multiply that by the radius?
    (0.9599310886)x(5000)= 4799.66 km

    So is that the height of the satellite? I'm kind of confused by the way the diagram is drawn.
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  5. #5
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    Quote Originally Posted by BobRoss View Post
    So I convert 55 to radians which gives me 0.9599310886 and then multiply that by the radius?
    (0.9599310886)x(5000)= 4799.66 km

    So is that the height of the satellite? I'm kind of confused by the way the diagram is draw.
    sorry, that is incorrect.

    you need to find  R first, then note that R = r + h

    the question wants you to find h.
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  6. #6
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by BobRoss View Post
    So I convert 55 to radians which gives me 0.9599310886 and then multiply that by the radius?
    (0.9599310886)x(5000)= 4799.66 km

    So is that the height of the satellite? I'm kind of confused by the way the diagram is drawn.
    Look at the equation again.

    \displaystyle s = r \theta \implies r = \frac{s}{\theta}

    This will give you the radius of the circle the satellite is in. That is, it will give you the distance from the satellite to the center of the Earth. How would you find the height from that?

    -Dan

    Edit: Not fast enough on the draw this time either. No wild West showdowns with skeeter for me!
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  7. #7
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    Okay so:
    R=8952/0.9599310886
    R=9325.66
    So that is the distance from the center of the planet to the satellite correct? So I subtract 5000 from that to get the height above the planet?
    h=4325.66 km

    Yay/nay?
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  8. #8
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    Quote Originally Posted by BobRoss View Post
    Okay so:
    R=8952/0.9599310886
    R=9325.66
    So that is the distance from the center of the planet to the satellite correct? So I subtract 5000 from that to get the height above the planet?
    h=4325.66 km

    Yay/nay?
    yes
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  9. #9
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    Great, thank you both for the help!
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