Calculating Freefall Acceleration on the Moon

AI Thread Summary
The discussion focuses on calculating the acceleration due to gravity on the Moon, given its mass and diameter relative to Earth. The participants explore the equations for gravitational force and acceleration, noting that the Moon's mass is one-hundredth that of Earth and its diameter is one-fourth. They derive the relationship between the gravitational acceleration on the Moon and that on Earth, ultimately determining that the Moon's gravity is approximately one-fourth that of Earth's. Confusion arises regarding the correct expression of the Moon's radius in terms of Earth's radius, which is clarified through further discussion. The final conclusion emphasizes the need to accurately substitute values to compute the gravitational acceleration on the Moon.
Ockonal
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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/
 
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Your mistake is that you dropped something. You were fine up to here:
Ockonal said:
g_earth = G×(M_earth/R_earth²)
g_moon = G×(M_moon / R_moon²)
Given that, what is g_moon / g_earth?
 
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?
 
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.
 
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 H said:
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 :(
 
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.
 
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' = ?
 
D H said:
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
yes!

now just substitute the values
 
  • #11
cupid.callin said:
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
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
cupid.callin said:
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
sorry i can't 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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