What are the odds that the Sun hits another star?

Question

The Sun moves around the Milky Way disk in the same direction as most of the other stars in our galaxy (prograde). But there are a number of older stars in the galactic halo that move in retrograde orbits, and some of them pass between the Sun and the center of the galaxy. What are the chances that the Sun will collide with another star, say in the next 5 billion years?

Answer 1

TL;DR: Virtually zero.

The distances between stars are HUGE and stars are tiny compared to the astronomical scales of distance between neighboring stars. The sun, is about 0.0000001 or one ten-millionth of a light year. The probability of a star (to be generous, say a $10 R_\odot$ star) colliding with the Sun is tiny.

Every star has a different velocity vector and different positions in space-time. The probability that their positions will intersect in a relatively short timescale is almost zero. Imagine throwing a tiny dart, and hitting a bullseye the size of an atom from several miles away. That still is larger than the probability of the Sun and some other star colliding in the near future (5 billion years is a tiny moment of time when it comes to events like these).

According to Wikipedia, it takes about 30 trillion years for a star to undergo a close encounter with another star. Even if the encounter is less than 1 AU, the stars would probably just pass by and not do anything special. For a complete collision and merge, you'd need the distances to be much, much smaller, about $0.1 R_\odot$.

Years from now

Event

3×1013 (30 trillion)

Estimated time for stars (including the Sun) to undergo a close encounter with another star in local stellar neighborhoods. Whenever two stars (or stellar remnants) pass close to each other, their planets' orbits can be disrupted, potentially ejecting them from the system entirely. On average, the closer a planet's orbit to its parent star the longer it takes to be ejected in this manner, because it is gravitationally more tightly bound to the star.

Source: https://en.wikipedia.org/wiki/Timeline_of_the_far_future

Also, according to Wikipedia:

While stellar collisions may occur very frequently in certain parts of the galaxy, the likelihood of a collision involving the Sun is very small. A probability calculation predicts the rate of stellar collisions involving the Sun is 1 in $10^{28}$ years.

Source: https://en.wikipedia.org/wiki/Stellar_collision#Stellar_collisions_and_the_Solar_System

Back to crude math, assuming an uncertainty of 2 AU, the probability given these parameters is equal to:

$$\dfrac{5 \cdot 10^9 \text{ years}}{3 \cdot 10^{13} \text{ years} \cdot 10^{24} \text{ stars in the universe}} \cdot \dfrac{0.1 R_\odot}{450 R_\odot} = \dfrac{1}{27,000,000,000,000,000,000,000,000,000,000} = \dfrac{1}{2.7 \cdot 10^{31}}$$

Warning: This is only a very crude estimate, don't take this as a "real, super-mathy" answer. But I still hope this helps.

Edit: That equation above is still probably too big. Asked a question about this: If two stars collide, what is the probability that they merge to form a single star?

Answer 2

As fasterthanlight says, the probability of our Sun colliding with another star in the galaxy is virtually nil. In fact, the probability of any star in the galaxy colliding with another (unrelated) star is very small.

Stars can and do collide, but they're stars that are already gravitationally bound to each other in binary or multiple star systems. And they generally don't collide until they're quite old. A star can pull material from a companion star, and in some cases that upsets the gravitational balance sufficiently that the stars merge, which can be rather explosive. Another option is that the stars' orbits decay via gravitational wave radiation. Even for neutron stars in tight orbits, which radiate gravitational energy at a relatively fast pace, this process takes a long time.

There's a lot of space between the stars in the galaxy. And even when whole galaxies collide, star collisions have a very low probability. Wikipedia says that when the Milky Way and Andromeda merge "the stars involved are sufficiently far apart that it is improbable that any of them will individually collide".

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The following may give you an idea of how low the star density of our galaxy is. According to Wikipedia, the mass of the Milky Way is somewhere between 0.8 and 1.5 trillion solar masses. That includes dark matter, which is a significant majority of the total mass, as well as the mass of loose interstellar gas and dust, so the actual mass of stars is quite a bit less. But let's go with the $1.5×10^{12} M_\odot$ figure, just to be generous. ;)

That article also says the diameter of the Milky Way's stellar disk is around 185 ± 15 thousand lightyears, depending how you define the outer edge. So let's use a radius of 85,000 lightyears. Also, the mean thickness of the galactic disk is around 1,000 lightyears.

Stars are made of hot plasma, so they're fairly tenuous in their outer regions. But they get quite dense in their cores, where most of the nuclear reactions happen. The mean density of the Sun is 1.41 g/cm³ (1,410 kg/m³), i.e., 1.41 times the standard density of water, but the density in its core is around 150 g/cm³, many times greater than the densest metal in terrestrial conditions.

Let's imagine that we could somehow homogenise and compress the Milky Way into a uniform disc, with its current radius, and with a density of 1g/cm³. So we're squishing that 1000 lightyear thickness of stars and everything else, down into a thin disk of radius 85,000 lightyears, with the same density as water.

Take a guess at how thick that disc would be.

1.469 millimetres.

You can check my calculation by plugging this formula into Google's search bar, which invokes the Google Calculator: (1.5e12 solar masses) / ((1 g/cm^3) * pi * (85000 lightyears)^2)

In contrast, if we squash the Sun down to a 1 g/cm³ disc of radius 30.1 au, the orbital radius of Neptune, we get a thickness of

31.2 metres

(1 solar mass) / ((1 g/cm^3) * pi * (30.1 au)^2)

Answer 3

Imagine that that there are 2 pigeons on LSD flying around the world. What are the chances that they would collide?

Colliding stars are less likely because if the stars were as big as pigeons, their average distance would be 200,000 kilometers.

Stars travel at 500.000 mph on average, so if they were birds, the birds would be flying at 0.000005 mph.

Stars are 10^11 times bigger than pigeons.

Here is an article about close encounters of our galaxy with other stars, i.e. Scholz'Star which passed about 50,000 AU from the sun, through the Oort cloud. https://www.discovermagazine.com/the-sciences/wandering-stars-pass-near-our-solar-system-surprisingly-often

That's like a pigeon passing 500 kilometers from another pigeon, being called a "close call".

The closest fly-by currently predicted is Gliese 710 will pass 5 times closer than Scholz star in 1.2 million years at 0.17 light years distance. It's currently 63 ly away.

I just checked this again, Wolfram sais that if the milky way was shrunk so it fits in the earth's orbit around the sun, there would be 100,000,000,000 birds(stars) flying at 1mm per minute, and 200,000 km in between the birds on average.