Gravitational force Sun/Sirius > Earth/Sun?

[andehpandeh]

I just watched the first 10 minutes of a documentary that seemed to touch on Walter Crutenberg's premise of our Sun being a binary twin of Sirius. Sirius A and B are separated by (at most) ~31 AU (1 AU = distance from Earth to Sun, 149,598,500 km). The Sirius system is 8.6 ly from Earth.

Distance traveled in a year = speed in km/sec X seconds
= 9,467,280,000,000 km = 1 Light Year

1 AU = 149,598,500 km

9,467,280,000,000 km
___________________ = 63,284.6 AU's in a LY
149,598,500 km

Now let's measure the gravitational force between the two systems:

F = Gm1m2
_________=
r^2
G is the gravitational constant, M1 is the mass of the Sun, M2 is the mass of the Sirius system ~ 3x the mass of our Sun.

F = (6.6726x10^-11)(1.989×10^30kg)(5.963x10^30kg)
___________________________________________________=
8.142x10^13km

= 1.194x10^23 Newtons
By comparison, the Sun/Earth force is 3.54x10^22 Newtons

My hypothesis was that the force between the Sun and Sirius would be insignificant given the vast expanse between them. Is there something the matter with my maths?

 

[Bandersnatch]

F = (6.6726x10^-11)(1.989×10^30kg)(5.963x10^30kg)
___________________________________________________=
8.142x10^13km

= 1.194x10^23 Newtons

This doesn't look right.
How did you come up with the number in the denominator?
Just by looking at it, it should be something like ~10^50 in the numerator, and ~10^32(in metres) in the denominator(~10^16m squared). So the force is in the order of 10^18N.

But even apart from that, remember that the force is proportional to mass. Divide that answer by the mass of one star to get the feel for the strength of the gravitational field produced by the other(aka the acceleration felt by a test particle) at that distance.

 

[Drakkith]

A gravitational force calculator gives me about 8x10¹⁶ Newtons of force between the two. This is an acceleration on the Sun of about 4.05x10^-14 m/s², and about half that for Sirius since it's about twice as massive as the Sun. Hopefully I got my input numbers correct.

Edit: Hmm. I just noticed you used the SYSTEM, not just the one star.

Ok, now I'm getting about 1.2x10¹⁷ Newtons of force, with 6x10^-14 m/s²of acceleration on the Sun, and 1/3 that for the Sirius system.

 

[D H]

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