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Addition to Extrasolar Planets
P a
2
For Extrasolar planets you can use
to get
a , the semi major axis.
To find the mass of the planet, use the following
formula.
M planet
v




 30,000m / s 
 P M
For explanation, and examples next page.
3
sun

3
The mass for 16 Cygni did not workout for Clevis or I. The curve
was not a sine curve, and I wonder if the fact that there is a second
star is possibly causing a three body problem, rather than 2 body.
This has taken me the better part of two days to go through all the
information.
The value of the parent star varied in data from .99 up to 1.1 solar
masses, and from a G3 to G5 star.
Lets find the mass of 16 Cygni . From last time:
Use
P a
2
2.18737303 years
3
to find
a
P= the period from the graph is
so a turned out to be 1.6844 au this answer was good.
To find the mass, use
M planet
v




 30,000m / s 
 P M
3
sun

.M is mass, P is the period in years, and v is the radial
velocity in m/sec.
To get v , notice the majority of the peaks are at about 50m/sec on the
left vertical side, and they go down to about –50 on the bottom.
Mass = 1.7 MJUP
Not Sinusoidal
(Min)
Orbit Period
2.2 yr
16 Cygni B
Velocity
Wobble
The best I can do here is estimate both are about 50 , so 50+50=100
and 100/2 =50 so use 50 for v. Some graphs are better to read then
this one was. Now I’m ready
M planet
M planet
v




30,
000
m
/
s


 50m / sec 


30,
000
m
/
s



3
 P M
3
sun


2.18737303  M sun 
M planet  .0016666661.2980984 M sun 
M planet  (.00216349)  M sun 
To change to Jupiter mass multiply by1047.45
M planet  (.00216349) 1047.45
M planet  2.16 M jupiter
Most accepted Answer is 1.7 not bad.
I also worked this problem for 51 Persi and got a to be .056459,
good answer, and Mplanet to be .54 Mjupiter . The real answer was
.45 Mjupiter. I found the curve for this one, and I used 68m/sec for v,
but I could have estimated better. The peaks and the low points are
not the same. Ignore the negative sign, add the numbers together ,
and divide by 2. That will be v.
Jim Honeycutt