My motivation to serve our country as an Officer in the United States Navy has grown out of my experience as an archaeologist. As an Archaeologist I was afforded the opportunity and privilege of leading field crews on surveys throughout the Desert West; covering hundreds of miles on foot through rough terrain in temperatures over 110ºF. That experience allowed me a small glimpse into the privilege and responsibility that comes from having individuals willing to follow your example and rely on your judgment. I would welcome the opportunity to earn that sense of responsibility again; to set an example, and to serve the individuals depending on me.
My entire life I have moved every three to four years, living in eleven different states throughout the United States. I believe these diverse experiences and travels have made me who I am today and I would welcome the opportunity to provide my children with the same type of experiences, to see our country and the world. The ability to provide this type of opportunity to my family, while being able to serve our country and its’ military personnel is absolutely a motivating factor in my desire to become a JAG Officer.
I do not take the commitment to military service I am making lightly; I recognize the extreme responsibility that comes with the commission of a Navy Officer. I feel compelled to serve my country and to be part of something bigger than myself. I have earned several honors in my academic pursuits, and have held positions of leadership, which would likely afford me the possibility of success down any path I pursue. However, my dream is to achieve that sense of honor, and commitment that I believe can only come from the privilege of military service.
Overall, I think you have a strong statement. However, I'd make the following adjustments
1. archeologist should be lowercase.
2. Avoid passive voice. "As an archaeologist I was afforded...to lead" I'd make this active. Just say "I led..."
3. Eliminate passive voice, e.g. "That experience allowed me..."
4. The second paragraph is awkward because it's three really long sentences. You should focus on varying the length of your sentences. A long sentence is fine. But following it up with a simple three or four word sentence will provide impact and make it easier to read. I would rework this paragraph because, in addition to the length of the sentences, your syntax could use improvement.
5. Lose the apostrophe -- "its"
6. First sentence, last paragraph, delete "I am making."
7. Third paragraph seems kind of generic. I realize that it's difficult to make these statements not sound generic/cliche, but if I were you, I'd tie-in at least one reference to archaeology in the final paragraph to bring it full circle. Make it more specific to you. It's hard to see the theme of the third paragraph as written.
All of the above are just minor suggestions. I think you're really on the right track. Good luck with your selection.