Everything Science Forum

I know that the sun and the moon have a gravitational pull on the earth, and that it changes with the lunar cycle depending on on the angles of the sun and the moon and so on.  However, I cannot find a way that I can measure this pull and how it varies day to day.  Please help.

Tanya

Mass has a property known as gravity, which we experience on earth as the force of gravity.

The magnitude of the force of gravity is given by

[tex] \large F = G \frac{m_1\,m_2}{r^2}[/tex]

where G is the Gravitational constant = 6.6742 x 10^-11 [tex]\frac{N m^2}{kg^3}[/tex] or [tex]\frac{m^3}{kg\,s^2}[/tex],

m₁ and m₂ are two masses, and r is the distance between the masses

The acceleration experience by the mass is just the force divided by that mass,

thus the acceleration of m₁ is the F/m₁ = a, or

[tex] \large a = G \frac{m_2}{r^2}[/tex]

So the acceleration of an object by the moon is just

[tex] \large a = G \frac{M_{moon}}{r^2}[/tex] where r is the distance between the moon (actually center of the moon) and the object.

Force is a vector, and multiple forces acting on the same point add vectorially.

Tanya,

Speaking as a professional astronomer, there ARE ways to measure the forces (if by measure you mean instrumentation, etc.) In fact, it is known that there are tides in the rocks of the Earth in the same way, but to a lesser amplitude, as the oceans. But it takes a good bit of doing to actually measure it.

Here are some websites on the matter.
http://www.whgrp.com/tms.htm
http://www.eclipse2006.boun.edu.tr/sss/paper02.pdf#search='gravitational%20tide%20measurement'
http://www.nap.edu/openbook/ARC000033/html/3.html

If you are looking to CALCULATE the forces, then Astronuc has given you the info you need to do it in its most basic form. There are some slight variations, due to things like the bodies in question not being perfect spheres or point masses, density variations in the bodies, etc. But in the main you can get it from that calculation.

Does this help answer your question?

Thank you, both of those helped a lot.  I am indeed trying to actually create a device to measure the variation in the pull of the moon.

Thanks again,
Tanya

you can use very sensitive gravity measuring device (like a spring) to measure it. That's actually the major correction factor for reliable gravity measurements

How bout this for a method: You have a pipe filled with vacuum:), then use
this stuff called piezoelectic film, its piezo material that is like saran wrap.
If you can isolate this pipe from ground vibrations or use a filter to filter out
anything like higher frequency than say, 0.1 Hz, leaving only the DC component,
the ends of the piezo film attached to some kind of connector like an RCA plug
one on each end of the pipe. The longer the pipe the better. Then the bending
of the piezo film will change as the moon passes overhead. The film would be
stretched as much as it can stand without deforming. The question here would
be what is the shortest pipe you can use and see a change in the piezo voltage. You can see where it would be bent down to the ground most strongly
when the sun and moon were on the opposite side of the earth and bent
less strongly when the sun and moon are overhead, as in a total eclipse.
Maybe it would be more sensitive if the film movement was measured by
a laser interferometer. Trying to go for the maximum sensitivity.
Its clear that for it to be sensitive enough to feel the moon directly, there can
be no moving objects for a good distance around the sensor. So we have the
detector at the bottom of a mine and we all leave and go to the surface for the
actual measurements.....

Doing the math, the moon's mass is 7.36 E22 Kg, the distance to the moon
is 225,000 (roughly, at closest approach) miles times 1600, or about
360 million meters. So using A=G*(m/r^2)  is 6.6742 E-11 * (7.36E22/3.6e86^2)
or 7.36E22/1.3E17=~ 566,150 * 6.6742E-11=3.7E-5. Is that M/S^2? Not sure
of the units. If its in units of accel, then 3.7E-5 times 9800 MM/S^2 (expressed
in MM rather than 9.8 M/S^2) gives 3.5 MM/S^2, about 1/27,000th of a G!
That would mean you need to measure one full G to an accuracy of 1 part in
30,000 or so. Thats a good trick, eh. Are the regular gravitational measurement
tools available to geologists and the like anywhere near that accurate?

Sonhouse,
Yes there are tools available that are a lot more accurate, and a well funded research lab might have one.

In the field of geology, depending on your speciality within the field, your tools vary dramaticly.