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anonymous
 one year ago
The sun’s mass is about 2.7 x 107 times greater than the moon’s mass. The sun is about 400 times farther from Earth than the moon. How does the gravitational force exerted on Earth by the sun compare with the gravitational force exerted on Earth by the moon?
anonymous
 one year ago
The sun’s mass is about 2.7 x 107 times greater than the moon’s mass. The sun is about 400 times farther from Earth than the moon. How does the gravitational force exerted on Earth by the sun compare with the gravitational force exerted on Earth by the moon?

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BAdhi
 one year ago
Best ResponseYou've already chosen the best response.1for easiness take newtons gravitational equation as, \[F \propto \frac{M}{r^2}\] (since \(m\), \(G\) are common for both scenarios) for moon=> \[F_m\propto \frac{M_m}{r_m^2}\] for sun, \[F_s \propto \frac{M_s}{r_s^2} \] by dividing both, get the equation

BAdhi
 one year ago
Best ResponseYou've already chosen the best response.1well this is a bit of a easy manipulation method, but if its confusing i'll describe, The gravitational field equation is,\[F=\frac{GmM}{r^2}\] If the gravity force between the moon and earth is \(F_m\) and mass of moon is \(M_m\) and the distance between moon and earth is \(r_m\) and the mass of the earth is \(m\) the above equation becomes,\[F_m = \frac{GmM_m}{r_m^2}= (Gm) \frac{M_m}{r_m^2}\] For force between the sun and earth is \(F_s\) and mass of the sun is \(M_s\) and distance is \(r_s\) , equation becomes,\[F_s = \frac{GmM_s}{r_s^2} = (Gm) \frac{M_s}{r_s^2}\] Is it clear so far?

BAdhi
 one year ago
Best ResponseYou've already chosen the best response.1now what you need is to compare \(F_s\) with \(F_m\) or get a value for \(\displaystyle \frac{F_s}{F_m}\) For that what should you do?

BAdhi
 one year ago
Best ResponseYou've already chosen the best response.1there you go.... any problems after that?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0only curious what do you plug into it so you can divide

BAdhi
 one year ago
Best ResponseYou've already chosen the best response.1first divide and see what terms get eliminated by division... Then try to plugin the values given as data... Remember what is given is as ratios too... For example, they say sun is \(2.7\times 10^7 \) times larger than moon in mass. Simply what that mean is, \(M_s = 2.7\times 10^7 M_m\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0F8/Fm F cancels rights

BAdhi
 one year ago
Best ResponseYou've already chosen the best response.1you mean \(\displaystyle \frac{F_s}{F_m} = \frac{s}{m}\) ??

BAdhi
 one year ago
Best ResponseYou've already chosen the best response.1oh dear... \(F_s\) and \(F_m\) are symbols as whole Just like \(A\) or \(B\) or any other symbols.. you jst cannot cut out parts of the symbol... simply what you are saying is like, \[\frac{V}{W} = \frac{1}{V}\] :P (by cutting out a apart of W with V since W is like two Vs)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0my bad so what do i do than

BAdhi
 one year ago
Best ResponseYou've already chosen the best response.1If you are not comfortable with the notation, Jst replace \(F_m,F_s, M_m, M_s, r_m, r_s\) with normal english letters such as \(a,b,c,d,e,f\) etc. and try out.. And please try to show what you've tried out

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no its not the symbols i just dont understand what im supposed to do to divide F8 by Fm

BAdhi
 one year ago
Best ResponseYou've already chosen the best response.1I have given you two equations for F_s and F_m. What you have to do is divide like, \(F_s = abc\), \(F_m = pqr\) \[\frac{F_s}{F_m} = \frac{abc}{pqr}\] Havent you done equation division before?

BAdhi
 one year ago
Best ResponseYou've already chosen the best response.1ok here is a problem solve it for me.. find \(\frac{F}{T}\) \(F=ba^2\) \(T=bc\)

BAdhi
 one year ago
Best ResponseYou've already chosen the best response.1I need the steps how you got there... not jst the answer..

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0idk how to explain it i just factored it out

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i know if you divide a equation by an equation you actually combine and multiply the variables

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0there are 2 b(s) hence 2b theres 1 c hence times c and 1 a^2 hence times a^2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so f8/fm becomes 2f8m

BAdhi
 one year ago
Best ResponseYou've already chosen the best response.1well thats not how it works... I think you should work out more with your equations and symbols. before getting into this kinda applications.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0its the last question i have than im done :(

BAdhi
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{F}{T} = \frac{ba^2}{bc}=\frac{a^2}{c}\] when the left hand side is divided same goes to the right hand side.. then if there are common symbols they jst cross out jst like what happen to the b here

BAdhi
 one year ago
Best ResponseYou've already chosen the best response.1Sorry I cannot jst give out the answer to this...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0im not asking you to just help me understand what i need to do

BAdhi
 one year ago
Best ResponseYou've already chosen the best response.1So would you mind showing us how to get the answer..

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes but i just need to know what am i pluging in as the right hand side against F8/Fm

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0nvm i know what i need to plug in

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ F _{8} }{ Fm }=\frac{ \frac{ (Gm)M _{m} }{ r _{m}^2} }{ \frac{ (Gm)M _{8} }{ r _{8}^2 } }=\frac{ \frac{ M _{m} }{ r _{m}^2 } }{ \frac{ M _{8} }{ r _{8}^2 } }\]

BAdhi
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{\left(\frac ab\right)}{\left( \frac c d\right)} = \frac a b \times\frac d c\] use this now

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ M _{m} }{ r _{m}^2 }*\frac{ M _{8} }{ r _{8}^2 }=2M _{m8}r _{m8}^4\]

BAdhi
 one year ago
Best ResponseYou've already chosen the best response.1note that when the division is changed to multiplication, c/d is changed to d/c...so what you've written there is wrong also... as i have mentioned before, \(M_s\times M_m\) cannot be further simplified to \(2M_{ms}\) (u can, maybe with some other algebra :P). It should jst be \(M_sM_m\) and treat \(M_s\) as a whole which cannot be separated and same goes to \(M_m\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohh ok so how would I write it @Badhi

BAdhi
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{M_m}{r_m^2}\frac{r_s^2}{M_s}\] and then adjust it like this, \[\left(\frac{M_m}{M_s}\right)\left(\frac{r_s}{r_m}\right)^2\]
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