Chapter 22, Problem 40Q

(a)

To determine

The distance to Sagittarius ${\text{A}}^{\ast }$. It is given that a length of $1600$ $\text{au}$ has an angular size of $0.2$ $\mathrm{arcsec}$.

(b)

To determine

The orbital period of S0-16 which is moves around Sagittarius ${\text{A}}^{\text{*}}$ in an elliptical orbit with a semi-major axis of $1680$ $au$. Use the figure(a).

Figure (a): Star orbiting around Sagittarius ${\text{A}}^{\text{*}}$

(c)

To determine

The methods by which the mass of S0-16 can be calculated, if the period and the semi-major axis of the star’s orbit is provided. Explain if it is not calculable.