state Newtown law of gravitation
Answers
every object in the universe attract toward each other with a force which is directly proportional to the product of their masses and inversnally to proportional the mean distance between them
Newton's Law of Gravitation
Idea: Newton's Universal Law of Gravitation states that any two objects exert a gravitational force of attraction on each other. The direction of the force is along the line joing the objects (See Fig.(7.3)). The magnitude of the force is proportional to the product of the gravitational masses of the objects, and inversely proportional to the square of the distance between them. For the two objects in Figure 7.3:
Figure 7.3: Gravitational Force
m1 exerts a force $\vec{F}_{12}^{}$ on m2 .
m2 exerts a force $\vec{F}_{21}^{}$ on m1 .
By Newton's third law:
$\displaystyle\vec{F}_{12}^{}$ = - $\displaystyle\vec{F}_{21}^{}$.
The magnitude of the gravitational force is:
F12 = G$\displaystyle{m_1 m_2 \over r^2}$. (22)
G is Newton's constant:
G = 6.67 x 10- 11 N m 2 /kg 2. (23)
Note:
The inertial mass of an object determines the amount of force needed to produce a given acceleration of that object. The gravitational mass determines the force of gravitational attraction between two bodies. In Newtonian mechanics, these two masses have no obvious connection with each other. Nonetheless, it was observed empirically that they are numerically equal. This remarkable fact was known for centuries, but remained unexplained until Einstein's General Theory of relativity.
Newton's gravitational constant is extremely small when expressed in terms of laboratory sized objects: the gravitational force between two 1 kg objects separated by 1 m is only 6.67 x 10- 11 Newtons.
For an object of mass m near the Earth's surface:
Fgrav = - G$\displaystyle{M_E\over R_E^2}$m = - mg (24)
where ME = 5.98 x 1024 kg is the mass of the Earth and RE = 6.38 x 106 m is the radius of the earth and
g $\displaystyle\equiv$ G$\displaystyle{M_E\over R_E^2}$ = 9.8 m/s 2 (25)
in agreement with the expression in Chapter 3.
Definition: Gravitional Potential Energy
Due to the gravitational force of attraction, any two objects with masses m1 and m2 located a distance r apart have the ability to do work. Hence they have potential energy. The gravitational potential energy of such objects is:
PE grav = - G$\displaystyle{m_1 m_2 \over r}$.
hope it helps u frnd
