Calculating the Barycentre Between Earth & Moon: A 14 Year Old's Journey

In summary, a young physicist (Will) asked if it was okay to post a question in a forum and proceeded to ask how far underground the barycentre between the moon and Earth was. Will gathered information on the masses of the Earth and Moon, the distance between them, and the radius of the Earth. He used a formula to calculate the distance from the Moon to the barycentre and then subtracted it from the distance between the Earth and Moon to get the distance from the Earth to the barycentre. He asked for confirmation on the accuracy of his math and if anyone knew the exact location of the barycentre. A link was provided as a reference.
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aguycalledwil
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First off, I'd like to apologize if this topic is against the rules. It's not a homework question, it's just something I decided to do in my spare time, so I figured it's okay to post here, but please tell me if not and I won't do it again.
Being a young physicist (14) I don't have much knowledge in math, so forgive me if this seems like a straight forward, simple question to you.

So my aim was to find how far underground the barycentre between the moon and the Earth was. I gathered several pieces of information as follows...

The mass of the Earth is 5.9742X10^24 KG
The mass of the Moon is 7.36X10^22 KG
The distance between the centre of the Earth and the centre of the Moon is 384,403 KM.
The radius of the Earth is 6378.1 KM

I then did the following...

r1 = a*m2/(m1+m2)

Where 'a' is the distance between the two objects, 'm1' is the mass of the first object and 'm2' is the mass of the second respectively.

So using my values I did...

r1 = 384,403*(5.9742*10^24)/((7.36*10^22)+(5.9724*10^24)). This gave me (supposedly) the distance from the moon to the barycentre. It came to 379,724 KM. I appreciate that it would have made a lot more sense for me to reverse some figures in the second half of the expression to give me the distance from the centre of the Earth to the barycentre, but I wasn't thinking properly. :p

Anyway, so I then did 384,403-379,724 to give me the distance from the centre of the Earth to the barycentre. This gave me 4679 KM. I then took this distance away from the radius of the Earth (6378.1 KM) to give me a final answer of 1699.1 KM underground.

So I was wondering if anyone could tell me how accurate/inaccurate my math is here? Does anyone know as a fact where the barycentre is?

Regards,
Will
 
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FAQ: Calculating the Barycentre Between Earth & Moon: A 14 Year Old's Journey

What is the barycentre between Earth and Moon?

The barycentre between Earth and Moon is the point in space where the two objects have equal gravitational pull on one another. It is often referred to as the "center of mass" or "center of gravity" between the two bodies.

How is the barycentre calculated?

The barycentre can be calculated using Newton's law of universal gravitation and the masses and distances of Earth and Moon. The formula is: barycentre distance = (Earth mass * Earth distance) / (Earth mass + Moon mass).

Why is the barycentre important to study?

The barycentre is important to study because it helps us understand the dynamics of the Earth-Moon system and the effects of their gravitational pull on each other. It also has practical applications, such as in spacecraft trajectories and satellite orbits.

How long did it take the 14-year-old to complete this journey?

The length of time it takes to complete the journey of calculating the barycentre between Earth and Moon can vary depending on the individual's level of knowledge and skill in mathematics and physics. However, with dedication and determination, a 14-year-old could potentially complete this journey in a few weeks or months.

What skills are needed to calculate the barycentre between Earth and Moon?

To calculate the barycentre between Earth and Moon, one needs a strong understanding of physics, particularly Newton's law of universal gravitation, and mathematical skills such as algebra and geometry. Patience and attention to detail are also important qualities to have in order to accurately complete the calculations.

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