# Mass and Density of Sun

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).

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## 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

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