# 6.5 Newton’s universal law of gravitation  (Page 6/11)

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## The cavendish experiment: then and now

As previously noted, the universal gravitational constant $G$ is determined experimentally. This definition was first done accurately by Henry Cavendish (1731–1810), an English scientist, in 1798, more than 100 years after Newton published his universal law of gravitation. The measurement of $G$ is very basic and important because it determines the strength of one of the four forces in nature. Cavendish’s experiment was very difficult because he measured the tiny gravitational attraction between two ordinary-sized masses (tens of kilograms at most), using apparatus like that in [link] . Remarkably, his value for $G$ differs by less than 1% from the best modern value.

One important consequence of knowing $G$ was that an accurate value for Earth’s mass could finally be obtained. This was done by measuring the acceleration due to gravity as accurately as possible and then calculating the mass of Earth $M$ from the relationship Newton’s universal law of gravitation gives

$\text{mg}=G\frac{\text{mM}}{{r}^{2}}\text{,}$

where $m$ is the mass of the object, $M$ is the mass of Earth, and $r$ is the distance to the center of Earth (the distance between the centers of mass of the object and Earth). See [link] . The mass $m$ of the object cancels, leaving an equation for $g$ :

$g=G\frac{M}{{r}^{2}}\text{.}$

Rearranging to solve for $M$ yields

$M=\frac{{\mathrm{gr}}^{2}}{G}\text{.}$

So $M$ can be calculated because all quantities on the right, including the radius of Earth $r$ , are known from direct measurements. We shall see in Satellites and Kepler's Laws: An Argument for Simplicity that knowing $G$ also allows for the determination of astronomical masses. Interestingly, of all the fundamental constants in physics, $G$ is by far the least well determined.

The Cavendish experiment is also used to explore other aspects of gravity. One of the most interesting questions is whether the gravitational force depends on substance as well as mass—for example, whether one kilogram of lead exerts the same gravitational pull as one kilogram of water. A Hungarian scientist named Roland von Eötvös pioneered this inquiry early in the 20th century. He found, with an accuracy of five parts per billion, that the gravitational force does not depend on the substance. Such experiments continue today, and have improved upon Eötvös’ measurements. Cavendish-type experiments such as those of Eric Adelberger and others at the University of Washington, have also put severe limits on the possibility of a fifth force and have verified a major prediction of general relativity—that gravitational energy contributes to rest mass. Ongoing measurements there use a torsion balance and a parallel plate (not spheres, as Cavendish used) to examine how Newton’s law of gravitation works over sub-millimeter distances. On this small-scale, do gravitational effects depart from the inverse square law? So far, no deviation has been observed. Cavendish used an apparatus like this to measure the gravitational attraction between the two suspended spheres ( m size 12{m} {} ) and the two on the stand ( M size 12{M} {} ) by observing the amount of torsion (twisting) created in the fiber. Distance between the masses can be varied to check the dependence of the force on distance. Modern experiments of this type continue to explore gravity.

what is thermodynamics
thermodynamic is a branch of physics that teaches on the relationship about heat and anyother form of energy
Emmanuel
if l cary box and stop is ther any work
no that because u have moved no distance. for work to be performed a force needs to be applied and a distance needs to be moved
Emmanuel
Different between fundamental unit and derived unit
fundamental unit are independent quantities that do not depend on any other unit while derived unit are quantities that depend on two or more units for it definition
Emmanuel
what is nuclear fission
hello
Shawty
are you there
Shawty
Shawty
what is a vector
vectors are quantities that have numerical value or magnitude and direction.
what is regelation
vector is any quantity that has magnitude and direction
Emmanuel
Physics is a physical science that deals with the study of matter in relation to energy
Hi
Jimoh
hello
Salaudeen
hello
Yes
Maxamuud
hi everyone
what is physics
physics is a physical science that deals with the study of matter in relation to energy
Osayuwa
a15kg powerexerted by the foresafter 3second
what is displacement
movement in a direction
Jason
hello
Hosea
Hey
Smart
haider
Explain why magnetic damping might not be effective on an object made of several thin conducting layers separated by insulation? can someone please explain this i need it for my final exam
Hi
saeid
hi
Yimam
Hi
Jimoh
An object made of several thin conducting layers separated by insulation may not be affected by magnetic damping because the eddy current produced in each layer due to induction will be very small and the opposing magnetic flux produced by the eddy currents will be very small
What is thê principle behind movement of thê taps control
while
Hosea
what is atomic mass
this is the mass of an atom of an element in ratio with the mass of carbon-atom
Chukwuka
show me how to get the accuracies of the values of the resistors for the two circuits i.e for series and parallel sides
Explain why it is difficult to have an ideal machine in real life situations.
tell me
Promise
what's the s . i unit for couple?
Promise
its s.i unit is Nm
Covenant
Force×perpendicular distance N×m=Nm
Oluwakayode
İt iş diffucult to have idêal machine because of FRİCTİON definitely reduce thê efficiency
Oluwakayode
It is difficult to have an ideal machine in real life situation because in ideal machines all the input energy should be converted to output energy . But , some part of energy is always lost in overcoming friction and input energy is always greater than output energy . Hence , no machine is ideal.
if the classica theory of specific heat is valid,what would be the thermal energy of one kmol of copper at the debye temperature (for copper is 340k)

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