Mass and Energy of Object that struck Earth and created moon

In summary, the object would have created two momentums: the Earth's spin angular momentum and the orbital angular momentum of the moon. The mass of the object would be 8.25(10)21 kg.
  • #1
bowlbase
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2

Homework Statement


This is third and last part of a question whose first part was solved on here earlier. Given the spin angular momentum of the Earth and the Orbital (around Earth) angular momentum of the moon calculate the mass of an object that if it hit the Earth at it's radius (glancing hit) would create these two momentums.


Homework Equations


L=RxMV
L=Iw
I=2/5 MR2


The Attempt at a Solution



I've gotten a final solution but just want to run the idea behind it to see if my logic makes sense.

The calculation of the spin momentum of the Earth was just L=Iw where w=2[itex]\pi[/itex]/P.
P is just the period of Earth's spin in seconds. I added that momentum to the moon's orbital momentum given by RxMV where R is the distance from moon to Earth and v=1000 m/s and of course the mass was that of the moon.

I added these two momentums together and set them equal to a new L. Then I just used the L=RxMv equation again with R= the radius of Earth and v the escape velocity of Earth (this was from the previous discussion and is correct). I found the mass to be 8.25(10)21 kg.

I expected a mass similar to the moon and this is what I got (minus an order of magnitude). Does this seem like the correct approach?

Thanks for the help. I can add the math but my question is more about method than calculations.
 
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  • #2
bowlbase said:

Homework Statement


This is third and last part of a question whose first part was solved on here earlier. Given the spin angular momentum of the Earth and the Orbital (around Earth) angular momentum of the moon calculate the mass of an object that if it hit the Earth at it's radius (glancing hit) would create these two momentums.


Homework Equations


L=RxMV
L=Iw
I=2/5 MR2


The Attempt at a Solution



I've gotten a final solution but just want to run the idea behind it to see if my logic makes sense.

The calculation of the spin momentum of the Earth was just L=Iw where w=2[itex]\pi[/itex]/P.
P is just the period of Earth's spin in seconds. I added that momentum to the moon's orbital momentum given by RxMV where R is the distance from moon to Earth and v=1000 m/s and of course the mass was that of the moon.

I added these two momentums together and set them equal to a new L. Then I just used the L=RxMv equation again with R= the radius of Earth and v the escape velocity of Earth (this was from the previous discussion and is correct). I found the mass to be 8.25(10)21 kg.

I expected a mass similar to the moon and this is what I got (minus an order of magnitude). Does this seem like the correct approach?

Thanks for the help. I can add the math but my question is more about method than calculations.
So let's get the figures straight:

Orbital speed of moon in its orbit, vm = 1000 m/s
Radius of moon orbit, Rm = 390,000,000 m.
Mass of moon, Mm = 7.34 x 10^22 kg

Rotational speed of the earth, ω = 2π/(24x3600) rad/s
Mass of the earth, Me = 5.97 x 10^24 kg
Radius of the earth, Re = 6,371,000 m.

Incoming speed of foreign body (fb) is the Earth escape velocity (assume 0 KE at infinite distance) which is vfb = 11,200 m/s

Angular momentum of system before collision is: Lbefore = Learth + Lfb = 0 + mfbvfbRe

Angular momentum of system after collision is: Lafter = Learth + Lmoon = 2MeRe2ω/5 + MmvmRm

If you equated those two angular momenta, which appears to be what you have done, then I would say you have done it correctly (but you should explain why they should be equal). I haven't worked out the numbers.

AM
 
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  • #3
Thanks for the comment. It's not often I get excited about what my physics tell me but being able to, even roughly, determine the components of such an event is pretty cool. Wish my EM class calculated things as interesting.

Thanks again!
 

1. What is the mass and energy of the object that struck Earth and created the moon?

The object that struck Earth and created the moon is estimated to have had a mass of about 1/10th the mass of Earth, which is equivalent to approximately 4.8 x 10^24 kilograms. The energy released from the impact is estimated to be equivalent to about 1.2 x 10^29 joules.

2. How did the impact of the object affect the Earth's mass and energy?

The impact of the object that created the moon had a significant effect on both the Earth's mass and energy. The Earth's mass was slightly increased due to the addition of the object's mass, while a significant amount of energy was released into the Earth's atmosphere, causing widespread destruction and altering the planet's environment.

3. Is the mass and energy of the moon related to the object that struck Earth?

Yes, the mass and energy of the moon are directly related to the object that struck Earth. The majority of the moon's mass is believed to have come from the object, while the energy from the impact played a crucial role in the moon's formation and characteristics.

4. How did the impact of the object affect the Earth's orbit?

The impact of the object that created the moon had a significant impact on the Earth's orbit. It is believed that the impact caused the Earth's rotation to speed up and tilt on its axis, leading to changes in the planet's orbit. This change in orbit also affected the Earth's climate and environment.

5. Could an impact like this happen again in the future?

While it is unlikely that an impact similar to the one that created the moon will occur again in the Earth's history, it is not impossible. Objects such as asteroids and comets are still present in our solar system, and the potential for future impacts cannot be ruled out entirely. However, scientists continue to monitor and track these objects to assess any potential risks and take preventive measures if necessary.

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