Mass of Star HD 179949: 8.77x10^31 kg

[kuahji]

In 2004 astronomers reported the discovery of a large Jupiter-sized planet orbiting very close to the star HD 179949 (hence the term "hot Jupiter"). The orbit was just {1 \over 9} the distance of Mercury from our sun, and it takes the planet only 3.09 days to make one orbit (assumed to be circular). What is the mass of the star? Express your answer in kilograms.

Ok, so I using a formula found in the book T=2$$\pi$$r$$^{3/2}$$/$$\sqrt{Gm}$$
Where r is the semi-major axis, G the gravitational constant, and m the mass of the star.

Solving for m
m=(2$$\pi$$r$$^{3/2}$$/T)^2/G

From the initial problem I found T=4.23x10^4 (converting 3.09 days/rev to seconds).

The orbital radius of Mercury in back of the text is 5.79x10^10, dividing that by nine yields 6.43x10^9.

Plugging in all the quantities I get 8.77x10^31kg. However this is not the correct answer. Any ideas where I could be going wrong?

 

[kuahji]

I was just using the wrong value for T, I calculated it wrong. It should have been 2.67x10^5 sorry. ^^

 

[thomate1]

It looks like you may have made a mistake in your conversion from days to seconds. 3.09 days should actually be 266976 seconds, not 4.23x10^4 seconds. When I plug in this value for T, I get a mass of 1.86x10^30 kg for the star HD 179949. This is a more reasonable value for the mass of a star, as 8.77x10^31 kg would be much larger than the mass of our own sun. I hope this helps!