# Mass and Energy of Object that struck Earth and created moon

## 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.

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$\pi$/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.

Andrew Mason
Homework Helper

## 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.

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$\pi$/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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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!