# Calculation example

Maximum line-of-sight velocity together with the orbital period gives limit on orbital radius, and then the oribital period and radius gives total mass.

Consider your ** fit** results. Note that the two stars must have the same orbiting period, so we take the average of

**and**

`vrfit1.b1`**:**

`vrfit2.b1`b = (vrfit1.b1+vrfit2.b1)/2;

Now you can calculate the orbiting period of the binary system: (in days)

T = (2*pi)/b

T = ...

The amplitude ** a1** in the sine function (the results you got by using

**) corresponds to the maximum orbital velocity of each star. This can be used to calculate the semi-major axis of each orbit around the center of mass.**

`fit`Be careful on transforming the units:

kilometer in AU units

km2au = 6.68e-9;

second in year units

s2yr = 3.17e-8;

Recall that the oribital period is (in year)

P = T/365

P = ...

The semi-major axis ** a_shallow** and

**are (in AU):**

`a_deep`a_shallow = vrfit1.a1*(km2au/s2yr)*P / 2 / pi a_deep = vrfit2.a1*(km2au/s2yr)*P / 2 / pi

a_shallow = ... a_deep = ...

*Note: What can a1 tell you about which star corresponds to which (shallow or deep)?*

Finally, the separation between the stars is

a = a_shallow + a_deep;

The total mass of the two stars: (in solar masses):

M = a^3 / P^2

M = ...

The fact that the velocity shifts of the lines are greater for one star than the other would imply unequal masses. Using the definition of center of mass, we can find the masses of the two components: (in solar masses)

M_shallow = M*a_deep / (a_shallow + a_deep) M_deep = M*a_shallow / (a_shallow + a_deep)

M_shallow = ... M_deep = ...