Gravitational acceleration from moon

[Irishwolf]

Hi ,
How could I calculate the acceleration of an object on the Earth's surface , say at the equator , from the influence of the moon , when the moon is directly overhead?

I have calculated the force of attraction from the moon to be 1.99 x 10^(20) N.

Now to find the gravitaional acceleration do I use ==> a=F/M
Where big M = mass earth?
I do I use the mass (m) of the moon?
Or is this not the way to calculate it?
-------------------------------------------------------
Another attempt of solving this was i used the formula for influence of moon on tides:
a= GMm/(R-r)^(2) - GMm/(R^(2))
and grav acc due to moon is 0.000001131 m/s^(2)
But someone said I should solve it with the above equation?

Help please

 

[Neandethal00]

Hi ,
How could I calculate the acceleration of an object on the Earth's surface , say at the equator , from the influence of the moon , when the moon is directly overhead?

I have calculated the force of attraction from the moon to be 1.99 x 10^(20) N.

Now to find the gravitaional acceleration do I use ==> a=F/M
Where big M = mass earth?
I do I use the mass (m) of the moon?
Or is this not the way to calculate it?
-------------------------------------------------------
Another attempt of solving this was i used the formula for influence of moon on tides:
a= GMm/(R-r)^(2) - GMm/(R^(2))
and grav acc due to moon is 0.000001131 m/s^(2)
But someone said I should solve it with the above equation?

Help please

I'm not sure I understand your question. If your question is what is the net acceleration of an object on Earth considering the gravitational effect of the moon, you may look at it with this formula:

a = GM_earth/R² - GM_moon/D²

M_earth = mass of earth
M_moon = mass of moon
R = Earth radius
D = distance from center of moon to the object.

 

[Irishwolf]

Hi yes that was my question thanks,
But why is that a different formula than the one used to calculate the moons influence on tides?

 

[Neandethal00]

Not sure about tide formula. What does that do?
Note, mass of the object is irrelevant. For tide, is there a
well defined mass? You can treat all ocean water as one massive object,
but then acceleration of what water? Our simple formula then may not be
very accurate.

 

[PJC01]

Hello,

Calculating the gravitational acceleration from the moon on an object on Earth's surface can be a bit complex, as it involves multiple factors such as the masses and distances of the Earth, moon, and object.

One approach to calculating this would be to use the formula for gravitational force between two objects:

F = G * (m1 * m2) / r^2

Where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.

In this case, m1 would be the mass of the moon and m2 would be the mass of the object on Earth's surface. The distance, r, would be the distance between the center of the moon and the center of the object on Earth's surface.

Once you have calculated the force of attraction between the moon and the object, you can then use the formula a = F / m2 to find the gravitational acceleration on the object.

Alternatively, you could also use the formula for gravitational acceleration due to an extended body:

a = G * M / r^2

Where M is the mass of the extended body (in this case, the Earth) and r is the distance from the center of the body to the point where the acceleration is being calculated (in this case, the Earth's equator). You would then need to subtract the gravitational acceleration due to the Earth alone from the total gravitational acceleration due to the Earth and the moon to find the specific influence of the moon.

I hope this helps clarify the process for calculating the gravitational acceleration from the moon on an object on Earth's surface. It is important to consider all the relevant factors and equations in order to arrive at an accurate calculation.