Asteroind Hitting The earth

  • Thread starter FahimP
  • Start date
  • Tags
    Earth
In summary, the problem involves finding the new angular speed of the Earth after an asteroid with a known mass and initial speed collides with it at a normal angle. Using the conservation of angular momentum and assuming no friction, the final angular speed can be calculated by considering the added mass and rotational inertia from the collision. The specific effects on the Earth's rotation will depend on the location and direction of the impact.
  • #1
FahimP
14
0

Homework Statement

The Earth has an angular speed of 7.272 10-5 rad/s in its rotation. Find the new angular speed if an asteroid (m = 1.17 1022 kg) hits the Earth while traveling at a speed of 1.41 103 m/s. The asteroid hits the Earth dead center.

We are just learning physics so this is all basics... we are ignoring friciton right now. I suppose this is just a basic angular momentum conservaton problem but I am having difficulty understanding it.

The Attempt at a Solution


I used the angular momentum conservation and this is what i have. I got stuck at the last part and I'm pretty confident i am right so far but i don't know what's next . Please help / advice / tips
My problem is that there are too many unknowns and I'm not sure if anything cancels .. do I need a second Equation ?

Ra= Radius of asteroid
Re = radius of earth
Me = Mas of Earth
Ma = mass of asteroid
Wf = Final speed
We= Initial angular speed of Earth
Wa = initial angular speed of asteroid

Lao + Leo = Laf + Lef
MaRa^2 Wf + 2/5MeRe^2 Wf = MaRaVa + 2/5 MeRe^2We
Wf( MaR^2 + 2/5MeR^2) = MaVaRa + 2/5 MeRe^2We
 
Last edited:
Physics news on Phys.org
  • #2
You have everything you need so think about it this way- at what incident angle does the asteroid hit the earth?

Assuming "dead center" means normal to the planet's surface (pointing to the imaginary center of the "spherical" planet), would its impact affect the Earth's rotation through momentum transfer, or simply add to the Earth's total mass (thus affecting its rotational inertia)?
 
  • #3
Mech_Engineer said:
You have everything you need so think about it this way- at what incident angle does the asteroid hit the earth?

Assuming "dead center" means normal to the planet's surface (pointing to the imaginary center of the "spherical" planet), would its impact affect the Earth's rotation through momentum transfer, or simply add to the Earth's total mass (thus affecting its rotational inertia)?

I have a question about this. When the asteroid hits the earth, won't the frictional force component during the impact generate a torque to the earth, thus slowing down its angular velocity, plus adding rotational inertia, slowing it further down? I am not sure about this, that's why I ask.
 
  • #4
Oldblood said:
I have a question about this. When the asteroid hits the earth, won't the frictional force component during the impact generate a torque to the earth,

The problem statement says the asteroid hits the Earth "dead center," which in my opinion precludes the possibility of the asteroid hitting the Earth at a tangent.

Of course this brings up another problem which I hadn't considered, WHERE on Earth does it hit? The effects will be different if it hits normal to the north pole versus at the equator, unless you make the assumption that the added mass can be approximated as being evenly distributed on the planet...

mheslep said:
thus slowing down its angular velocity, plus adding rotational inertia, slowing it further down? I am not sure about this, that's why I ask.

This would all depend on which direction the asteroid hit. Assuming it hit at a tangent, it could either speed up rotation, slow it down, or tilt the rotational axis. Since according to the problem the asteroid is hitting normal to the Earth's surface, the effects should be seen in rotational inertia only, but it has occurred to me you need to make an assumption the added mass will be considered as evenly distributed around the "spherical" (also an assumption) planet.

In any case, it seems to me that the speed of the asteroid is irrelevant when you assume it hits the surface at a normal, and the mass is evenly distributed.
 
  • #5

Wf = (MaVaRa + 2/5 MeRe^2We) / (MaRa^2 + 2/5MeRe^2)

First of all, it is important to note that this is a hypothetical scenario and in reality, there are many other factors that would come into play in the event of an asteroid hitting the Earth. However, for the sake of this problem, we can approach it using basic principles of angular momentum conservation.

Your initial attempt at a solution is on the right track. However, there are a few things that need to be clarified. Firstly, the initial angular speed of the asteroid (Wa) should be the same as the angular speed of the Earth (We), since they are both in orbit around the same point. Secondly, the initial angular speed of the Earth (We) is not given in the problem, so we need to find a way to eliminate it from the equation.

One approach could be to use the fact that the Earth's angular speed (We) is directly related to its radius (Re) and its linear speed (Ve) through the equation We = Ve/Re. This equation can be derived from the definition of angular speed, which is the change in angular displacement over time. In this case, the Earth's angular displacement remains constant, so the change in its angular speed is directly proportional to the change in its linear speed. By substituting this equation into your original equation, we can eliminate We and solve for the final angular speed (Wf).

Another approach could be to use the fact that the angular momentum of a system is conserved, which means that the sum of the initial angular momenta must be equal to the sum of the final angular momenta. In this case, we can set the initial angular momentum of the system (Lao + Leo) to be equal to the final angular momentum (Laf + Lef) and solve for Wf.

Whichever approach you choose, make sure to carefully consider the units of each term in the equation to ensure that they are consistent. It may also be helpful to draw a diagram and label all the variables to help visualize the problem. I hope this helps and good luck with your physics studies!
 

1. What is an asteroid?

An asteroid is a small, rocky object that orbits the Sun. They are typically composed of rock, metal, and sometimes ice, and range in size from a few feet to hundreds of miles in diameter.

2. How often do asteroids hit the Earth?

Asteroid impacts are relatively rare events, with only a few large impacts occurring every million years. However, smaller impacts from asteroids and meteoroids happen more frequently, with an estimated 100 tons of material falling to Earth every day.

3. Can an asteroid wipe out all life on Earth?

It is possible for a large enough asteroid to cause mass extinction events, as evidenced by the extinction of the dinosaurs 66 million years ago. However, the probability of a catastrophic impact is very low in the near future.

4. How do scientists track asteroids and predict potential impacts?

Scientists use telescopes and radar to track the orbits of known asteroids and identify potential impact risks. They also use mathematical models to predict their future paths and determine the likelihood of an impact.

5. What measures are being taken to prevent an asteroid from hitting the Earth?

NASA and other space agencies have programs in place to identify and track potential impact risks, and are continuously monitoring and researching ways to prevent or mitigate asteroid impacts. This includes developing plans for deflecting or destroying incoming asteroids.

Similar threads

  • Introductory Physics Homework Help
Replies
2
Views
5K
  • Introductory Physics Homework Help
Replies
12
Views
6K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
6K
  • Astronomy and Astrophysics
Replies
4
Views
2K
  • Astronomy and Astrophysics
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
11K
Back
Top