Two-body problem

On 11/03/2014 6:11 PM, Yousuf Khan wrote:
On 11/03/2014 12:24 PM, Steve Willner wrote:
In article ,
Yousuf Khan writes:
So you're taking the unknown star to be the B5

No, the known star was the B5. The unseen companion works out to be
more massive, presumably a black hole. That depends, of course, on
my having used the correct formula, which I still don't vouch for.

Oh, you're saying that the visible star, the B5-type star, is 5.8 solar
masses, while the invisible mass star is 7.25 solar masses? That's an
interesting way to turn the problem around.

Yousuf Khan

I found another way of doing the problem at this site:

Properties of Stars
http://www.astronomynotes.com/starprop/s10.htm

But unfortunately, this also depends on the knowing the relative
velocities of the two stars to each other. There's no way around this,
if you don't know the relative velocity of both stars, then you can't
calculate both of their masses.

Yousuf Khan

In article ,
Yousuf Khan writes:
if you don't know the relative velocity of both stars, then you can't
calculate both of their masses.

That seems a strange assertion after I've shown you how to do the
calculation.

If you want to check, try calculating the period of a binary with
stars having 5.8 and 13.6 solar masses and the smaller star having a
semi-major axis of 8 AU. (The semi-major axis of the larger star
will be 8*5.8/13.6 = 3.4 AU.) I still don't swear the formula I used
is right, but the basic method is, and the correct formula should be
easy enough to work out from Newtonian gravity and a little algebra.

By the way, it is obvious at first glance that the unseen star has to
be more massive than the visible star. And one minor correction:
looking again, I see _AAQ_ gives 5.9 solar masses for a B5V star, so
if you care, put in the correct number and redo the calculation.

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Help keep our newsgroup healthy; please don't feed the trolls.
Steve Willner Phone 617-495-7123
Cambridge, MA 02138 USA

In article ,
Yousuf Khan writes:
I found another way of doing the problem at this site:
Properties of Stars
http://www.astronomynotes.com/starprop/s10.htm

Yes, that's probably easier to understand than my way.

But unfortunately, this also depends on the knowing the relative
velocities of the two stars to each other.

Not at all. The key equations are given in the text:

(mass1 + mass2) = (separation distance)^3/(orbital period)^2
and
(mass1) * (C.M. distance1) = (mass2) * (C.M. distance2)

You will also need to recognize that (separation distance) is the sum
of the two C.M. distances. Let one mass be that of the visible B
star and solve for the remaining unknown mass.

I'm not going to do the algebra, but the result I got is close but
not exactly right. (It's easy to plug my earlier result into the
equations above and check.)

--
Help keep our newsgroup healthy; please don't feed the trolls.
Steve Willner Phone 617-495-7123
Cambridge, MA 02138 USA

On 18/03/2014 2:57 PM, Steve Willner wrote:
In article ,
Yousuf Khan writes:
I found another way of doing the problem at this site:
Properties of Stars
http://www.astronomynotes.com/starprop/s10.htm

Yes, that's probably easier to understand than my way.

But unfortunately, this also depends on the knowing the relative
velocities of the two stars to each other.

Not at all. The key equations are given in the text:

(mass1 + mass2) = (separation distance)^3/(orbital period)^2
and
(mass1) * (C.M. distance1) = (mass2) * (C.M. distance2)

You will also need to recognize that (separation distance) is the sum
of the two C.M. distances. Let one mass be that of the visible B
star and solve for the remaining unknown mass.

I'm not going to do the algebra, but the result I got is close but
not exactly right. (It's easy to plug my earlier result into the
equations above and check.)

I think maybe the main problem I am having is figuring what is the right
mass of a B5-type star is, when calculating, it came out out to 7.25
which is pretty close to what I'd expect any generic B-type star to be.
But your source said a B5 star would be around 5.8 solar masses.

I was unfortunately not able to find a table of star masses which I
could reference from the Internet. But you had a good old-fashioned book
from which to reference it. But I needed to be able to verify the mass
of B5 stars myself, as I like to be able to verify my own work later.
But searching on the Internet is so much about proper search terms as
anything else!

I originally did a search for "mass of B5 star", and Google spit out a
whole bunch of data about Babylon 5 the TV show! Pretty fun, as I'm a
fan of that show, but not what I was looking for.

But now, I finally did a more generic search term of "table of star
masses", and finally came up with this result:

World Builders Star Tables for Mass, Luminosity, etc
http://www.world-builders.org/lesson...rTables_B.html

Above table confirmed B5 stars are 5.9 solar masses, pretty close to
what you said. So hopefully, somebody is going to be able to make a
search of this discussion in the future, and they'll know which site to
go to from now on.

Yousuf Khan

In article ,
Yousuf Khan writes:
I think maybe the main problem I am having is figuring what is the right
mass of a B5-type star is, when calculating, it came out out to 7.25

You can't calculate it from the data given; you have to look it up
from an external source. The data given in the original problem
determine a combination (not the simple sum) of the two masses; if
you know either one of them, you can find the other.

World Builders Star Tables for Mass, Luminosity, etc
http://www.world-builders.org/lesson...rTables_B.html

At a first glance, the masses look identical to the ones in the _AAQ_
table I used. I think they may originate from a 1981 study
http://adsabs.harvard.edu/abs/1981A%26AS...46..193H
but haven't compared in detail.

Above table confirmed B5 stars are 5.9 solar masses,

I wrote 5.8 originally but later corrected to 5.9, the actual value
in the table. The uncertainty is much larger than 0.1 solar mass.

The World Builders site looks like a fine resource, based on only a
brief glance.

--
Help keep our newsgroup healthy; please don't feed the trolls.
Steve Willner Phone 617-495-7123
Cambridge, MA 02138 USA

On 20/03/2014 5:38 PM, Steve Willner wrote:
I wrote 5.8 originally but later corrected to 5.9, the actual value
in the table. The uncertainty is much larger than 0.1 solar mass.

The World Builders site looks like a fine resource, based on only a
brief glance.

Yup, I thought so too.

Yousuf Khan