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Math Help - gravitational force

  1. #1
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    gravitational force

    need help with this please. not sure if there is an equation for gravitational force, and which one to use.

    The drawing shows one alignment of the sun, earth, and moon.
    The gravitational force SM that the sun exerts on the moon is perpendicular to the force EM that the earth exerts on the moon.
    mass of sun = 1.99 1030 kg,
    mass of earth = 5.98 1024 kg,
    mass of moon = 7.35 1022 kg.

    The distances shown in the drawing are rSM = 1.50 1011 m and rEM = 3.85 108 m. Determine the magnitude of the net gravitational force on the moon.

    in Newtons

    What is rSM and rEM?

    need some help with the equations please.

    heres whats going on: http://img91.imageshack.us/img91/2585/p424cw9.gif
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  2. #2
    Junior Member Spimon's Avatar
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    I reckon you'll be able to do this one if you put ur mind to it.

    For this question, we need to find the force of attraction between the Earth and the Moon, and also the force of attraction between the Sun and the Moon. From there we can find the total force on the moon.

    It will help a lot if you draw a quick diagram of the information you know for this one. You should basically have a triangle with the Sun, Moon and Earth at each corner.

    We know the mass of each and the distance between the Eart and the Moon, so plug that info into the formula and get that force.
    Remember the formula F = (M1*M2)/(R^2)?

    We know the mass of the sun and the moon, but not the distance separating the, so let's find that first.
    From your diagram, we can find a triangle with sides 385,108m and 1,501,011m. Using Pythagoras' Theorem we can find the hypotenuse.
    Now we have the distance between the Sun and the Moon and the mass of each, so we can apply the formula to find the force of attraction.

    Now we have 2 forces acting on the moon. By adding these vectors, we can find the total force acting on the moon.
    Let me know if you're not familiar with vectors and I'll explain more.

    Give it a shot and post your answer.
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  3. #3
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    okay, i guess i need a further explanation, because i'm still not understanding parts of this.

    i thought the distance between the sun and moon was known: The distances shown in the drawing are rSM = 1.50 x 10^11 m

    sorry about the notation before.

    also, why do i need the hypotenuse for this problem?

    thankyou.
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  4. #4
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    Quote Originally Posted by Spimon View Post
    I reckon you'll be able to do this one if you put ur mind to it.

    For this question, we need to find the force of attraction between the Earth and the Moon, and also the force of attraction between the Sun and the Moon. From there we can find the total force on the moon.

    It will help a lot if you draw a quick diagram of the information you know for this one. You should basically have a triangle with the Sun, Moon and Earth at each corner.

    We know the mass of each and the distance between the Eart and the Moon, so plug that info into the formula and get that force.
    Remember the formula F = (M1*M2)/(R^2)?

    We know the mass of the sun and the moon, but not the distance separating the, so let's find that first.
    From your diagram, we can find a triangle with sides 385,108m and 1,501,011m. Using Pythagoras' Theorem we can find the hypotenuse.
    Now we have the distance between the Sun and the Moon and the mass of each, so we can apply the formula to find the force of attraction.

    Now we have 2 forces acting on the moon. By adding these vectors, we can find the total force acting on the moon.
    Let me know if you're not familiar with vectors and I'll explain more.

    Give it a shot and post your answer.
    I thought the equation wa : F = G(M1*M2)/(R^2)

    I am having problems with this one too.
    Last edited by La_Diabla; June 25th 2008 at 07:30 AM. Reason: input my equations and work
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by rcmango View Post
    okay, i guess i need a further explanation, because i'm still not understanding parts of this.

    i thought the distance between the sun and moon was known: The distances shown in the drawing are rSM = 1.50 x 10^11 m

    sorry about the notation before.

    also, why do i need the hypotenuse for this problem?

    thankyou.
    Quote Originally Posted by La_Diabla View Post
    I thought the equation wa : F = G(M1*M2)/(R^2)

    I am having problems with this one too.
    First off, spimon made a simple typo. The formula for Newtonian gravity is indeed
    F = \frac{Gm_1m_2}{r^2}

    So let's define a coordinate system with +x horizontally to the left and +y upward.

    The force between the Earth and the Moon will be
    F_{ME} = \frac{GM_EM_M}{r_{EM}^2}
    and since this is an attraction it will be in the negative y direction.

    The force between the Sun and the Moon will be
    F_{MS} = \frac{GM_SM_M}{r_{SM}^2}
    and since this is an attraction it will be in the positive x direction.

    Now you need to add these forces vectorally.

    -Dan
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