How to Compute the Mass of Sgr A* Using Star Orbits?

[leonne]

Homework Statement

New observations of the stars orbiting the black hole at the Galactic Center (Sgr
A*) have improved the measurements. Here are the latest results from Gillessen et
al. (2009) for star S0-2: period P = 15:8 yr, semimajor axis a = 1025 AU, and
eccentricity e = 0:880; and for star S0-16: P = 47:3 yr, a = 2130 AU, and e = 0:963.
(a) Compute the mass (in units of solar masses) of Sgr A* implied by the new results.
Do the two stars give a consistent answer?

Homework Equations

M=(4pie^2 a^3)/Gp^2

The Attempt at a Solution

For s0-2 i first converted AU to cm and years to seconds then 4pie^2(1.53e16)^3 /(6.6743e-8)(498599430)^2
and got 8.52e16 grams then 4284399 Mo is this correct the formula i used to find mass of the black hole?

 

[fzero]

I think you're missing a factor of pi, double check the formula

M=(4 pi^2 e^2 a^3)/Gp^2

got 8.52e16 grams then 4284399 Mo

Something's fishy because 4 * 10⁶ M_\odot is the right order of magnitude, but 8.52e16 grams is 17 orders of magnitude smaller than a solar mass.

My computation is 3.34 10⁶ M_\odot. The WA expression is

http://www.wolframalpha.com/input/?i=4+%28pi^2%29+%28.880%29^2+%281025+*+149597870.700+*10^3%29^3+%2F%28+%286.67428+*+10^%28-11%29%29+%2815.8+*31556952++%29^2+%281.988+*+10^30++%29

if you want to compare.

 

[leonne]

ok thanks ill check again later

 

[leonne]

formula is correct what i have well that is to find the mass of the interior orbit of the star also its 8.52e39 idk why i always write down something wrong when i do physics lol