Neutron star question

How close to Earth would a 10km neutron star have to pass to cause
global problems (orbit changes etc)?

Hi Rick Answer is "Very close" Bert

Rick wrote:
How close to Earth would a 10km neutron star have to pass to cause
global problems (orbit changes etc)?


"Neutron stars typically have masses of around 1-2 solar masses and
diameters of approximately 10 km."

http://csep10.phys.utk.edu/astr162/l...n/neutron.html

So it had better not get anywhere near as close to us as the Sun, or
off we go!

Double-A

"Rick" wrote in message
k.net...
How close to Earth would a 10km neutron star have to pass to cause
global problems (orbit changes etc)?

A neutron star weighs in somewhere between 1.4 and 3 solar
masses. An expression for the radius of a neutron star is:

R = 0.114*h^2 / (G*mp^(8/3)) / M^(1/3)

h is Planck's constant
mp is the mass of the proton
G is Newton's gravitational constant
M is the mass of the neutron star

(see: http://jrfcomet.homestead.com/files/tech/herx1a.htm)

By the above formula a 10km diameter neutron star would weigh
in at about 28 solar masses, a value impossibly high for a
neutron star. What you'd have is a black hole on your hands.

Moving on, even assuming a more typical mass for the neutron
star it is difficult to answer your question with any degree
of accuracy because the amount of orbit perturbation will
depend not only on proximity but on duration of the passage
of the object. It would also depend to a large extent on the
particular trajectory with respect to the plane of the solar
system (ecliptic).

Because the solar system bodies interact gravitationally,
and comprise a mathematically chaotic system, a small
perturbation of an outer planet could eventually cause major
changes for, and even ejection of, inner planets. You'd
want to perform a statistical analysis of a great many
simulated scenarios.

Here's an idea for a quick-and-dirty estimate though. Consider
the tidal forces generated across the solar system by the neutron
star, and in particular, the net induced tidal force between the
Sun and Jupiter. I choose Jupiter because being the largest
planet, changes in its orbit would have the greatest amount of
influence, in a short time, on the rest of the planets. Set some
arbitrary limit on the size of this force as compared to the
Sun-Jupiter gravitational force, and see what kind of distance
falls out.

Gravitational force: G*Ms*Mj/rj^2

Tidal force: G*Mn*(Ms/d^2 - Mj/(d+rj)^2)

d is the Sun-neutron star distance
rj is the radius of Jupiter's orbit
Ms is the mass of the Sun
Mj is the mass of Jupiter
Mn is the mass of the neutron star

Simplifying assumptions:
Mn = a*Ms (mass of neutron star is a times mass of Sun)
Mj = 1/1000 Ms
d = k*rj (measure distance to neutron star in terms of
Sun-Jupiter distances)

I get an expression for the ratio of forces that looks like:

Ratio = a*(999*k^2 + 2000*k +1000)/((k+1)^2 * k^2)

If the neutron star weighs in at 3 solar masses, then for the
tidal force to be less than 1% of the gravitational force, the
distance to the neutron star would have to be some 550 Sun-Jupiter
distances, or nearly 3000 AU.

A neutron star is one step away from a BH in creating a universe. Bert