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    Mass and Density of Sun

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    a) Calculate the mass of the sun from the radius of the earth's orbit (1.5 x 10^11 m)., the earth's period in its orbit, and the Universal Gravitational Constant, G.

    b) What is the density of the sun and how does it compare with the density of the earth? (The sun's radius is 6.96 x 10^ 8 m).

    © BrainMass Inc. brainmass.com December 24, 2021, 5:04 pm ad1c9bdddf
    https://brainmass.com/physics/orbits/mass-density-sun-26675

    SOLUTION This solution is FREE courtesy of BrainMass!

    ^ denotes power
    E denotes to the power of 10 ; thus 2.0077 E +30 is 2.0077 x 10 ^ 30

    F= (G M m) / r ^2 ---- Law of Gravitation ----(1)
    where
    G= gravitational constant=
    M= mass of the sun
    m= mass of the earth
    r= radius of earth's orbit

    Now F is also equal to m v ^2 /r = centripetal force= m w ^2 r ^2/r
    as v=w r where w is the angular velocity
    Simplifying
    F= m w ^2 r

    But w = 2pi /T
    where T = earth's period in its orbit
    Thus F= m (2 pi /T) ^2 r
    or F=(4 pi ^2 / T ^2) r ----(2)

    Equating Equation (1) with (2)

    F= (G M m) / r ^2 = (4 pi ^2 / T ^2) r

    Cancelling m from both sides and rearranging the terms
    M= (4 pi ^2 / T ^2) (r ^3 /G)

    Now
    r=1.5 x 10^11 m=
    T=365 days = 365 x 24 x 3600 sec= 31536000 sec
    G= 6.673 x 10^ -11 N-m^2/Kg ^2

    Solving
    M= 2.0077E+30 Kg

    Answer: Mass of the Sun= 2.0077 x 10^30 Kg

    (b) What is the density of the sun and how does it compare with the density of the earth? (The sun's radius is 6.96 x 10^ 8 m).

    Volume of the Sun =( 4/3 ) pi R ^3
    R= sun's radius= 6.96 x 10^ 8 m
    Therefore Volume of Sun= 1.41227E+27 m^3

    mass of the sun = 2.0077E+30 Kg (obtained above)

    Density= Mass of the sun / Volume of the sun = 1421.62 Kg/m^3

    In comparison density of earth=5.519 x 10^3 kg/m3

    i.e. the density of earth is around 4 times the density of sun

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 5:04 pm ad1c9bdddf>
    https://brainmass.com/physics/orbits/mass-density-sun-26675

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