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Moon gravity

  • Thread starter Ockonal
  • Start date
  • #1
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Homework Statement


Mass of the Moon is nearly less in 100 times than Earth's, and the diametr is less in 4 times.
Find the acceleration of free falling at the Moon.

Homework Equations


F = G×((M×m)/R²)
g = 9.8N

The Attempt at a Solution


M_moon = M_earth / 100
D_moon = D_earth / 4
R_moon = D_moon / 2 = D_earth / 8

g_earth = G×(M_earth/R_earth²)
g_moon = G×(M_moon / R_moon²)
=>
M_earth = (g×R_earth²) / G
M_moon = (g×R_earth²) / G / 100
...
g_moon = g_earth / 25
But the answer is wrong. I think my mistake is in diameter passing and converting it into radius. Help me, please/
 

Answers and Replies

  • #2
D H
Staff Emeritus
Science Advisor
Insights Author
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Your mistake is that you dropped something. You were fine up to here:
g_earth = G×(M_earth/R_earth²)
g_moon = G×(M_moon / R_moon²)
Given that, what is g_moon / g_earth?
 
  • #3
30
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so:
g_moon / g_earth =

M_moon × R_earth²
-------------------
M_earth × R_moon²

Now I'm passing data instead of *_moon:

(M_earth/100) × R_earth²
----------------------
M_earth × (D_earth / 4)

How to make it easier?
 
  • #4
30
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so:
Code:
g_moon / g_earth =
 
M_moon × R_earth²
-------------------
M_earth × R_moon²
Now I'm passing data instead of *_moon:
Code:
(M_earth/100) × R_earth²
----------------------
M_earth × (D_earth / 4)
How to make it easier?

-----
I did this:

Code:
  M_earth × R_earth²
----------------------
          100
----------------------
M_earth × 2 × R_earth
----------------------
              8
=>
R_earth / 25

But R_earth shouldn't be presented.
 
  • #5
D H
Staff Emeritus
Science Advisor
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If the diameter of the Moon is roughly 1/4 of the diameter of the Earth, what can you say about the radius of the Moon in terms of the radius of the Earth?
 
  • #6
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If the diameter of the Moon is roughly 1/4 of the diameter of the Earth, what can you say about the radius of the Moon in terms of the radius of the Earth?
D_moon = 1/4 D_Earth
R_moon = (1/4 D_Earth)/2

I'm confused :(
 
  • #7
D H
Staff Emeritus
Science Advisor
Insights Author
15,393
683
You just expressed the Moon's radius in terms of the Earth's diameter. I asked you to express the Moon's radius in terms of the Earth's radius. So, try again, please.

Once you have that figured out, go back to computing g_moon / g_earth.
 
  • #8
1,137
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you know that g=Gm/r2

now for earth

g = GM/R2

for moon, g' = GM'/R'2

you know that M' = M/100 and D' = D/4

so R' = ?
 
  • #9
30
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You just expressed the Moon's radius in terms of the Earth's diameter. I asked you to express the Moon's radius in terms of the Earth's radius. So, try again, please.

Once you have that figured out, go back to computing g_moon / g_earth.
As I understand:
D/4 = Moon's diametr, so:
R/4 + R/4 = D/4
So radius is smaller in 4 times?
 
  • #10
1,137
0
yes!!!

now just substitute the values
 
  • #11
30
0
now just substitute the values
Didn't understand right, maybe:
Code:
g_moon = G × ( M_earth / 25 × R_earth² )
g_earth = G × ( M_earth / R_earth² )

g_moon / g_earth = 
    M_eath × R_earth²
-----------------------   =
M_earth × 25 × R_earth²

1/25
 
  • #12
1,137
0
the ' ones are for moon


g = GM/R2

for moon, g' = GM'/R'2

you know that M' = M/100 and D' = D/4

so R' = R/4


Code:
g' = G(M/100)
      _______
        R/4

so ... g' = <something> GM/R[sup]2[/sup]
        g' = <something> g
 
  • #13
30
0
the ' ones are for moon
Code:
g' = G(M/100)
      _______
        R/4

so ... g' = <something> GM/R[sup]2[/sup]
        g' = <something> g
Sorry, I can't understand from where did you get GM/R² in
Code:
g' = G(M/100)
      _______
        R/4
 
  • #14
1,137
0
sorry i cant give answer ,,, got 2 warnings for it

i just rearranged the eqn and dividing the numbers i can

separate GM/R² ... and as you know from eqn of earth GM/R² = g

eqn of earth ... sounds fascinating!!
 

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