Effects of perpendicularly-approaching asteroid on Earth

In summary, we are discussing the hypothetical situation of an enormous, spherical, homogeneous body with a density of 3000 kg/m^-3 appearing 25,000 light years from the Milky Way. It is approaching the Milky Way perpendicular to its equatorial plane and headed towards Earth. We are looking at its effects on Earth in terms of orbital dynamics and gravitation, ignoring the fact that such an object cannot exist in general relativity. According to classical physics, the object would immediately start perturbing Earth's orbit and could potentially pull Earth out of its orbit entirely. However, due to the limitations of our ability to detect small gravitational forces, it is difficult to determine exactly when this would happen.
  • #1
Aquohn
4
0
Assume the following hypothetical situation: an enormous body, 20,000 ly in diameter (I recognise that 'asteroids' per se tend to be smaller), approaches the Milky Way, perpendicular to its equatorial plane, and headed straight for planet Earth, or at least on a trajectory where it will definitely collide with the Earth at some point. Assume that the body (the 'evil space rock', from now on) is a perfectly spherical, homgenous body of density 3000 kg m^-3, that magically appeared 25,000 ly from the Milky Way (i.e. its gravitational waves have only just begun propagating towards the Earth). At what distance would it begin to have any effect on the Earth? At what distance would it upset the Earth's orbit enough to cause destructive climate change and a consequent extinction event? At what distance would it extract the Earth from orbit entirely and begin pulling it towards itself?

And, as a side-query, what would happen if the evil space rock were to impact (or rather, get sucked into) Sagittarius A*? What if it was aimed there instead of at Earth?
 
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  • #2
A body with similar properties would be a black hole, and black holes have a fixed relation between size and density - with a size of 20000 light years, their density would be smaller.

Your object cannot exist - at least not in general relativity, so it is pointless to ask about predictions of that theory.

You are aware that 20000 light years is about the distance between us and the galactic center?
 
  • #3
Why can't it exist? HVC 127-41-330 is 20,000 ly across, but it consists 80% of dark matter and 20% of hydrogen. Is the evil space rock too massive, or what?

At any rate, I'm actually looking more for answers on the classical physics (orbital dynamics, etc.) side of things. If we were to ignore the impossibilities of the objects existence, what would its effect be on the planet, in terms of basic kinematics and gravitation (F = -GMm/r^2, etc.)?
 
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  • #4
Aquohn said:
At any rate, I'm actually looking more for answers on the classical physics (orbital dynamics, etc.) side of things. If we were to ignore the impossibilities of the objects existence, what would its effect be on the planet, in terms of basic kinematics and gravitation (F = -GMm/r^2, etc.)?

You just stated it. There's no limit on how far away or how close the object has to be. Every star you see in the sky is tugging on you because of its gravitational pull. Likewise, your presence in the universe gravitationally affects every star you see in the sky (and even stars you can't see).

The only limit is how weak of a force can you detect. For example, if you take the gravitational force between Jupiter and the Sun, and then add in the gravitational force between you and Jupiter, does your calculator display enough digits to display the difference?

To figure out when it would pull the Earth out of its orbit, just plug in the masses involved and determine what distance is needed to equal the gravitational force between the Sun and the Earth. Although that wouldn't tell you when the Earth's orbit began to become horribly distorted. It will start perturbing the orbit immediately. You might arbitrarily choose some other boundary, such as when the Earth is becoming unacceptably cold for unacceptably long periods of time, etc.
 
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  • #5
Aquohn said:
Why can't it exist? HVC 127-41-330 is 20,000 ly across, but it consists 80% of dark matter and 20% of hydrogen. Is the evil space rock too massive, or what?
Yes, a rock is much denser than a cloud. I never would have considered calling a cloud an "object".
 
  • #6
OK, then what about a black hole absorbing a large mass, like the evil space rock? Would the emissions (if any) have any appreciable effect on the Earth?
 
  • #7
HVC 127-41-330 is a very good vacuum - just not as good as its environment.

The gravity of other objects influence our solar system as soon as tidal forces become relevant - if everything is accelerated in the same way, it does not matter.

Tidal accelerations are of the order of ##\frac{GM}{r^3}d## where d is the distance between objects in the solar system, r is the distance to the massive object and M is the mass of this object. This has to be compared with ##\frac{Gm}{d^2}## where m is the mass of our sun. Setting both equal gives ##\frac{M}{r^3} \approx \frac{m}{d^3}##. As an example, an object with 1000 solar masses would seriously disturb planetary orbits in a distance of ~10 times the orbital radius of planets, but does not matter (at least not for the orbits of planets) at ~100 times this distance.

Based on this abstract, ~10^8 solar masses should be a good upper limit on the mass of HVC 127-41-330.
This corresponds to a density of ##5\cdot 10^{-23}\frac{kg}{m^3}## (and 26 orders of magnitude below the value given in the first post). To get significant tidal effects, this mass would have to be in a distance of less than 1000 times the orbital radius. Using Neptune, this corresponds to about 0.5 light years.
Obviously, a cloud of 20000 light years diameter cannot be 0.5 light years away. We would have to pass through the cloud and come close to some mass concentration inside (like a star or a black hole) to notice its gravitational influence on the solar system at all.
 
  • #8
your sense of scale is off..if it were like you explained in the first posts you could pick up electrons from atoms by holding a water melon next to your target atom.

I don't think numbers are absolutely needed to "solve" this one...its rather observational and logic.
An object so large cannot affect details on an object as small as our planet.
It would pull on half the galaxy but not on our clouds and weather baloons.
 
  • #9
BobG said:
To figure out when it would pull the Earth out of its orbit, just plug in the masses involved and determine what distance is needed to equal the gravitational force between the Sun and the Earth.
...
OK, I'm feeling reeeeaaaally embarrassed right now.
 

1. How likely is it for an asteroid to approach Earth perpendicularly?

The likelihood of an asteroid approaching Earth perpendicularly depends on various factors such as the size and trajectory of the asteroid, as well as the position of Earth in its orbit. While it is possible for an asteroid to approach Earth perpendicularly, the chances of this occurring are relatively low.

2. What would be the potential effects of a perpendicularly-approaching asteroid on Earth?

The effects of a perpendicularly-approaching asteroid on Earth can vary depending on the size and composition of the asteroid. It could potentially cause significant destruction on impact, leading to tsunamis, earthquakes, and other natural disasters. It could also have long-term effects on the Earth's climate and ecosystem.

3. How does the angle of approach affect the impact of an asteroid on Earth?

The angle of approach can greatly impact the effects of an asteroid on Earth. A perpendicular approach would result in a more direct impact and greater destructive force compared to an asteroid approaching at a shallower angle. The angle of approach also determines the location of impact and the potential for a global or localized disaster.

4. Can we predict the effects of a perpendicularly-approaching asteroid on Earth?

Scientists use various methods and technologies to track and predict the path of asteroids. However, accurately predicting the exact effects of a perpendicularly-approaching asteroid on Earth is challenging due to the many variables involved. Nevertheless, ongoing research and advancements in technology are improving our ability to predict and prepare for potential asteroid impacts.

5. What measures are in place to protect Earth from a perpendicularly-approaching asteroid?

There are several measures in place to protect Earth from potential asteroid impacts. These include early detection and tracking systems, as well as potential mitigation strategies such as deflecting the asteroid's path or destroying it before impact. However, further research and collaboration are essential to improving our ability to protect Earth from potential asteroid threats.

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