Answer
(a) The parallax angle is 0.018''
(b) The parallax angle is $(5.0\times 10^{-6}) {^{\circ}}$
Work Step by Step
We can use this equation to find the parallax angle of the star:
$D = \frac{d}{\phi}$
(Note that D is the distance to the star, d = 1 AU, and $\phi$ is the parallax angle measured in radians.)
$\phi = \frac{d}{D} = \frac{1~AU}{56~pc} = \frac{1.5\times 10^{11}~m}{(56)(3.09\times 10^{16}~m)}$
$\phi = 8.67\times 10^{-8}~radians$
We can convert this angle to arc seconds and degrees:
$\phi = (8.67\times 10^{-8}~radians)(\frac{3600\cdot 360''}{2\pi}) = 0.018''$
$\phi = (8.67\times 10^{-8}~radians)(\frac{360^{\circ}}{2\pi}) = (5.0\times 10^{-6})^{\circ}$
(a) The parallax angle is 0.018''
(b) The parallax angle is $(5.0\times 10^{-6}) {^{\circ}}$
