Mission 05
Weigh the Black Hole
You cannot see Sagittarius A* and you certainly cannot put it on a scale. What you can do is watch something fall around it. S2 is a young star that swings past the centre of the galaxy every sixteen years, and its orbit is the most direct evidence that four million Suns sit inside a space smaller than our own planetary system.
Track the star
Twenty years of infrared images, one point each. The orbit only appears once you have enough of them.
Fit the ellipse
The long axis is the widest your points spread. The period is how many years it takes to come back round. The hole sits at a focus, not the centre.
Divide
Mass in Suns is the axis in AU cubed, over the period in years squared. That is Kepler, and it weighs anything.
Keep observing. One arc is not an orbit.
At its closest S2 passes 120 AU from the hole at 7,650 km per second — about two and a half per cent of the speed of light.
4,297,000 M☉ · GRAVITY collaboration