Question

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?

Answer 1

for 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

Answer 2

im a little lost

Answer 3

well 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?

Answer 4

yes

Answer 5

now 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?

Answer 6

divide F8/Fm

Answer 7

there you go.... any problems after that?

Answer 8

only curious what do you plug into it so you can divide

Answer 9

first 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,
\(M_s = 2.7\times 10^7 M_m\)

Answer 10

8/m?

Answer 11

whats that?

Answer 12

F8/Fm F cancels rights

Answer 13

you mean \(\displaystyle \frac{F_s}{F_m} = \frac{s}{m}\) ??

Answer 14

yah...is that wrong

Answer 15

oh 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)

Answer 16

my bad so what do i do than

Answer 17

If 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

Answer 18

no its not the symbols i just dont understand what im supposed to do to divide F8 by Fm

Answer 19

I 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?

Answer 20

idk

Answer 21

ok here is a problem solve it for me..

find \(\frac{F}{T}\)

\(F=ba^2\)
\(T=bc\)

Answer 22

2b*c*a^2

Answer 23

I need the steps how you got there... not jst the answer..

Answer 24

idk how to explain it i just factored it out

Answer 25

i know if you divide a equation by an equation you actually combine and multiply the variables

Answer 26

there are 2 b(s) hence 2b theres 1 c hence times c and 1 a^2 hence times a^2

Answer 27

correct?

Answer 28

so f8/fm becomes 2f8m

Answer 29

\[2F _{8}m\]

Answer 30

well thats not how it works...

I think you should work out more with your equations and symbols. before getting into this kinda applications.

Answer 31

its the last question i have than im done :(

Answer 32

\[\frac{F}{T} = \frac{ba^2}{bc}=\frac{a^2}{c}\] 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

Answer 33

Sorry I cannot jst give out the answer to this...

Answer 34

im not asking you to just help me understand what i need to do

Answer 35

ohhh ok i get it

Answer 36

So would you mind showing us how to get the answer..

Answer 37

yes but i just need to know what am i pluging in as the right hand side against F8/Fm

Answer 38

nvm i know

Answer 39

nvm i know what i need to plug in

Answer 40

\[\frac{ F _{8} }{ Fm }=\frac{ \frac{ (Gm)M _{m} }{ r _{m}^2} }{ \frac{ (Gm)M _{8} }{ r _{8}^2 } }=\frac{ \frac{ M _{m} }{ r _{m}^2 } }{ \frac{ M _{8} }{ r _{8}^2 } }\]

Answer 41

?

Answer 42

good

Answer 43

\[\frac{\left(\frac ab\right)}{\left( \frac c d\right)} = \frac a b \times\frac d c\] use this now

Answer 44

\[\frac{ M _{m} }{ r _{m}^2 }*\frac{ M _{8} }{ r _{8}^2 }=2M _{m8}r _{m8}^4\]

Answer 45

?

Answer 46

?

Answer 47

note 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 \(M_m\)

Answer 48

ohh ok so how would I write it @Badhi

Answer 49

\[\frac{M_m}{r_m^2}\frac{r_s^2}{M_s}\] and then adjust it like this,
\[\left(\frac{M_m}{M_s}\right)\left(\frac{r_s}{r_m}\right)^2\]