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What is this constant in the gravitational acceleration formula?

  1. Oct 21, 2011 #1
    1. The problem statement, all variables and given/known data

    Hey all, I'm doing an assignment and I was given the formula below, but I'm unsure what one of the constants is.

    2. Relevant equations

    Acceleration = - μEr/r3

    3. The attempt at a solution

    Below the formula it says "where μE is the gravitational constant for the Earth and r is the position vector of the vehicle". But this is talking about a satellite orbiting Earth, so it can't be 9.8m/s/s, can it?

    Am I meant to use μE = u*m1*m2/r2 to find it?

    I've used the 'geocentric gravitational constant' elsewhere in the assignment, but it used a different symbol, this isn't it either is it?

    Cheers
     
  2. jcsd
  3. Oct 21, 2011 #2

    ehild

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  4. Oct 21, 2011 #3

    NascentOxygen

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    Last edited by a moderator: Apr 26, 2017
  5. Oct 21, 2011 #4

    ehild

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    The correct formula you asked about is

    [tex]\vec a = -\mu_e \frac{\vec r}{r^3}[/tex]

    [itex]\vec r [/itex] is the position vector of a satellite or any point-like mass with respect to the centre of Earth, and [itex]\vec a [/itex] is its gravitational acceleration. The formula is a special case of the Universal Law of Gravity,

    [tex]\vec F = -G \frac{m_1 m_2 \vec r}{r^3}[/tex]

    the force a point mass 1 exerts on an other point mass 2 at distance r. The force is parallel and opposite to the vector [itex]\vec r[/itex] pointing to mass 2 from mass 1.
    G is the gravitational constant G= 6.67259 ˙10-11 Nm2kg-2.

    If the first mass is the Earth, Gm1=GMearthe.

    ehild
     
  6. Oct 21, 2011 #5
    Is that 'Gravitational Constant' the 'Universal Gravitational Constant (6.67*10-11' Nascent?
     
  7. Oct 21, 2011 #6
    Ignore my above post.

    That makes sense ehild! Because F = ma, a = F/m. You remove the mass of the satellite from your second formula and exchange F for a. Leaving you with a = G*mE*r/r3.

    Thanks!
     
  8. Oct 21, 2011 #7

    ehild

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    All right, I see you got it.

    ehild
     
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