Parallax to distance: 1 / 0.38 = 2.6315 pcy_utsumi wrote:How can this be solved? I know it has to do with Kepler's laws, but I keep getting a very large answer..
Suppose that the mass of Sirius B is 0.98 solar masses, and the semi-major axis between Sirius A is 7.5 arcsec observed from Earth, and that we are viewing the system face-on. Calculate the period for the Sirius system to complete one orbit in Earth years.
(The previous questions gave the following information: mass of Sirius A = 2.18 solar masses, Sirius parallax (observed from Earth) = 0.38 arcsec, apparent magnitude of Sirius A = -1.47.)
The answer is 48.4 +/- 1.0 years.
Set up a triangle, and the semi major axis = 2.6315 * tan ( 7.5 arcsec ) = 9.568 * 10^-5 parsecs = 19.73625 AU
Since p^2 = a^3 when period is in years and length of the semi-major axis is in then:
p = sqrt ( a^3 )
p = sqrt ( 19.73625^3 )
period = 87.68 years
(yay I can do these now!)