What Is the Correct Calculation for the Mass of the Sun?

[SpeedBird]

hey there, i am having trouble with what should be a really easy question!
*********
calculate the mass of the sun assuming that the Earth's orbit is circular
and with a radius of 1.5 * 10^8 km

i got the period of the Earth's orbit around the sun in seconds:
60*60*24*365.25

then used the formula:

T = ((4*Pi^2*r^3)/(G*M))^2

rearranging in terms of M

i change the radius of the orbit to metres instead of kilometres before putting
it into the formula.

but the answer i get is 1.9 * 10^30 kg
and i think the answer should be in the order of 10^40 kg

can anyone suggest where i might be going wrong?

thanks

Nik

 

[stunner5000pt]

This is Kepler's Law

$$T^2 = \frac{4 \pi^2}{GM} r^3$$

rearranged into

$$M = \frac{4 \pi^2}{GT^2} r^3$$

now sub in and see what s wrong

 

[SpeedBird]

i see i wrote the formula wrong in my original post!
i meant raised to the power of 1/2 at the very end.
i am still getting 2 * 10^30 as my answer..
this might be the correct answer and the question is just
unrealistic?

Nik

 

[stunner5000pt]

the question is not unrealistic, the mass of the sun is 1.99x10^30 kg the answer of the book of 10^40 is wrong (or you're looking at the wrong question)

 

[SpeedBird]

ahh thank you! i found the value from a search on google :-S
it didnt even cross my mind that the value was wrong.

thank you very much!

Nik