Determine the mass of the Earth from the known period and distance of the Moon.

Question

anonymous · Answer

@agent0smith  please help me I am getting the wrong answer for some reason

anonymous · Answer

I got 4.49 x 10 ^ 27 kg

agent0smith · Answer

show your work...

agent0smith · Answer

Use the period and distance to find the moons orbit speed v. Then equate gravitational force with centripetal force.

anonymous · Answer

M earth = 4 (pi)^2 r^3 / G T^2 

4 (pi) ^2 (384 x 10 ^6) ^3/ (6.67 x 10^-11) (86400)^2

= 4.49 x 10^27 kg

anonymous · Answer

i dont know what i did wrong

anonymous · Answer

the numbers for radius G is given in the book and I used the Period as a hint of time and converted to seconds

agent0smith · Answer

using period as 27.3 days (maybe that was your error idk)$$\Large T = \frac{ 2 \pi r }{ v }$$ use this to find v = 1022.9m/s

then equate centripetal force with graviational between earth/moon$$\Large \frac{ m v^2 }{ r} = \frac{ G m M }{ r^2 }$$ to find M = 6.02*10^24 kg, with the actual mass being 5.97*10^24 kg.

agent0smith · Answer

4.49 x 10^27 kg is way too large, idk what you did wrong but you're off by a factor of 1000

anonymous · Answer

how did you find the velocity? I am confused..what do you mean by 27.3 days

agent0smith · Answer

I plugged numbers into that equation, using the moon's period as 27.3 days (converted to seconds).

anonymous · Answer

i think this was a trick question because it the actual is 5.98 x 10 ^24 kg and thats what showed up when I put it in the answer

anonymous · Answer

why would you use days and not hours, to get time I did 24hr x 60 min x 60 sec

agent0smith · Answer

It's not. You can see from my answer that you can get pretty close.

anonymous · Answer

yes I see it now, thank you so much!

agent0smith · Answer

No prob. You can prob use kepler's laws but i prefer doing it that way, using the gravitational and centripetal force.

anonymous · Answer

yeah I think that is easier since we get graded on the way we show our work and the professor wants to see what we learned from class and use it towards homework, we cant use new stuff that we haven't learned yet..they are pretty harsh with hw grading =/

anonymous · Answer

thanks again =D

agent0smith · Answer

Well i'm sure you've learned centripetal and gravitational force, right? You can basically get them from a diagram... |dw:1382236648850:dw|

anonymous · Answer

yes thats all we have learned in chapter 5

loser66 · Answer

do you know what is wrong with yours? at T , it is (27.4 days * 86400 second/day)^2 . yours is lag of 27.4 days. That's why you get the wrong answer.

agent0smith · Answer

ohh yeah you just have seconds in one day...

anonymous · Answer

ohhh