A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

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?

  • This Question is Closed
  1. BAdhi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 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

  2. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    im a little lost

  3. BAdhi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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?

  4. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

  5. BAdhi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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?

  6. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    divide F8/Fm

  7. BAdhi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  8. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  9. BAdhi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  10. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    8/m?

  11. BAdhi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    whats that?

  12. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    F8/Fm F cancels rights

  13. BAdhi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  14. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yah...is that wrong

  15. BAdhi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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)

  16. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    my bad so what do i do than

  17. BAdhi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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

  18. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  19. BAdhi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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?

  20. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    idk

  21. BAdhi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok here is a problem solve it for me.. find \(\frac{F}{T}\) \(F=ba^2\) \(T=bc\)

  22. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    2b*c*a^2

  23. BAdhi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  24. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    idk how to explain it i just factored it out

  25. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  26. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  27. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    correct?

  28. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so f8/fm becomes 2f8m

  29. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[2F _{8}m\]

  30. BAdhi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    well thats not how it works... I think you should work out more with your equations and symbols. before getting into this kinda applications.

  31. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    its the last question i have than im done :(

  32. BAdhi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 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

  33. BAdhi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  34. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  35. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ohhh ok i get it

  36. BAdhi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  37. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  38. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    nvm i know

  39. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    nvm i know what i need to plug in

  40. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  41. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ?

  42. BAdhi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    good

  43. BAdhi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  44. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  45. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ?

  46. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ?

  47. BAdhi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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 \(M_m\)

  48. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ohh ok so how would I write it @Badhi

  49. BAdhi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  50. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.