# Estimate prevalence of ʻOumuamua-style interstellar obects inside Jupiter orbit now that C/2019 Q4 (Borisov) is found?

Now we know two of them, so maybe it's not an outlier.

We have two points so we can draw a line. How many similar macroscopic objects should be zipping through space at ~30 km/sec so that we would see one of these passing inside the orbit of Jupiter once every two years? I don't really know what units this should be expressed with. Maybe it's 1 / (km^2 * year) - the frequency of such a body coming through any random square kilometer of empty space in a year of time.

What's the "capture cross section" of intra-Jupiter orbit? I imagine that since the Sun affects trajectories of bodies coming near it, drawing them closer as they pass by, intra-Jupiter orbit will see much more bodies than a circle of same area in empty space. How large is this effect for ʻOumuamua-like bodies? I expect this is to be a unitless coefficient. Is it neligible? Is it 5x? 10x? 1000x?

Sorry if my question is not clear enough.

• List of Hyperbolic comets: en.wikipedia.org/wiki/List_of_hyperbolic_comets (those with eccentricity >1) – Wayfaring Stranger Sep 18 at 17:49
• Most of those are barely hyperbolic because of gravitation perturbances inside Solar system. They, in turn, may become scouts if they ever arrive to other systems. – alamar Sep 19 at 9:46

The enhancement of a cross-section due to gravitational focusing is given by $$\sigma_{\rm eff} = \pi a_J^2 \left(1 + \frac{2GM_{\odot}}{a_J\ v^2}\right),$$ where $$a_J$$ is the semi-major axis of Jupiter's orbit (assumed circular), $$v$$ is the relative velocity (at infinity) and I have ignored the mass of Jupiter.

Thus, using $$v=30$$ km/s (as specified in the question) the term in brackets is the gravitational focusing enhancement of the cross-section and equals 1.38.

We now assume an isotropic velocity distribution and a homogeneous density of such objects of $$n$$ per unit volume. The flux of such particles is $$f =n v \sigma_{\rm eff}$$.

If $$f = 0.5$$ yr$$^{-1}$$, then $$n \sim 5 \times 10^{12}$$ per cubic parsec.

• Thank you for backing me up with math! I wonder how much error I had in my napkin calculations. – alamar Sep 17 at 21:31

I had to write my own code to calculate this, since I could not find any tools to solve two-body problem.

From my simulation it seems that Jupiter orbit cross section is 6.5 AU, assuming radius of Jupiter orbit as 5 AU. Seems like a tiny difference, but surface-wise it's 1.7x increase. This assuming 20 km/s, it's smaller for faster scouts.

This means one scout passes through a 6×10^24 square meters per year. Thus we can expect 30 million of these passing through every square light year.

During that year, scout will travel at least 600 million km. This means there's maybe 2×10^24 scouts in our galaxy.

Each scout probably weighs 2×10^9 kg. This means there are 4×10^33 kg worth of them in our galaxy. That's 2,000 suns.