How Fast Will the Asteroid Hit Earth?

In summary, a NASA satellite has detected a 5.05×109 kg asteroid approaching Earth with a velocity of 619 m/s and a distance of 5.15×106 km. The formula for conservation of energy, Ep = -GMm/r, should be used when determining the asteroid's speed upon impact, taking into account the distance between the asteroid and Earth's center of mass.
  • #1
squib
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A NASA satellite has just observed an asteroid that is on a collision course with the Earth. The asteroid has an estimated mass, based on its size, of 5.05×109 kg. It is approaching the Earth on a head-on course with a velocity of 619 m/s relative to the Earth and is now 5.15×106 km away. With what speed will it hit the Earth's surface, neglecting friction with the atmosphere?

I tried Ep + Ek = Ek + Ep, but no luck, is there a problem with my formula?

Ep = GMm/r r being the distance between the com of the two.
 
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  • #2
squib said:
I tried Ep + Ek = Ek + Ep, but no luck, is there a problem with my formula?
The formula is OK, assuming you are applying conservation of energy to the asteroid.
Ep = GMm/r r being the distance between the com of the two.
Don't forget the minus sign: Ep = -GMm/r
 
  • #3


The formula you used, Ep + Ek = Ek + Ep, is not the correct formula for this scenario. The formula you need to use is the conservation of energy equation, which states that the total energy (potential energy + kinetic energy) of a system remains constant. In this case, the system is the asteroid and the Earth.

The formula for conservation of energy is:

E = Ep + Ek = constant

Where:
E = total energy
Ep = potential energy
Ek = kinetic energy

In this problem, we can assume that the asteroid has no initial potential energy, as it is far away from the Earth. Therefore, the equation becomes:

E = Ek = constant

Using this equation, we can solve for the final kinetic energy of the asteroid just before impact. The final kinetic energy will be equal to the initial potential energy, which is given by the formula you mentioned, Ep = GMm/r.

So, we can write:

Ek = GMm/r

Now, we can plug in the values given in the problem:

Ek = (6.67×10^-11 Nm^2/kg^2)(5.98×10^24 kg)(5.05×10^9 kg)/(6.38×10^6 m) = 5.01×10^15 J

Since we now have the final kinetic energy of the asteroid, we can use the formula for kinetic energy, Ek = 1/2mv^2, to solve for the final velocity (v) of the asteroid just before impact.

Rearranging the formula, we get:

v = √(2Ek/m)

Plugging in the values, we get:

v = √(2(5.01×10^15 J)/(5.05×10^9 kg)) = 6.26×10^3 m/s

Therefore, the asteroid will hit the Earth's surface with a speed of approximately 6.26 km/s. It is important to note that this is a theoretical calculation and does not take into account the effects of atmospheric friction, which would likely decrease the speed of the asteroid slightly. Nevertheless, it is clear that the asteroid will hit the Earth with a tremendous amount of energy and could potentially cause significant damage. It is important for NASA to continue monitoring the asteroid and come up with a plan to prevent a collision with Earth.
 

1. What is potential energy?

Potential energy is the energy that an object possesses due to its position or state. It is stored energy that has the potential to be converted into other forms of energy, such as kinetic energy.

2. What are some common examples of potential energy?

Some common examples of potential energy include a stretched rubber band, a compressed spring, a raised object, and chemical energy in food or fuel.

3. How is potential energy calculated?

The formula for calculating potential energy is PE = mgh, where PE is potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height or distance from the reference point.

4. How does potential energy differ from kinetic energy?

Potential energy is the energy that an object has due to its position or state, while kinetic energy is the energy that an object possesses due to its motion. Potential energy can be converted into kinetic energy and vice versa.

5. How can potential energy problems be solved?

Potential energy problems can be solved by using the formula PE = mgh and plugging in the given values for mass, height, and acceleration due to gravity. It is important to pay attention to the units and use the correct formula for the specific problem.

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