the Sun and their semi-major axes. Planet a ( m ) (years) a Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune . . .
. . . - - - - Unit Gravitation where r is the unit vector from M towards M as shown in Figure .
, and G is the Gravitational constant that has the value of N m kg , and r is the distance between the two masses M and M . In Figure . , the vector F denotes the gravitational force experienced by M due to M . Here the negative sign indicates that the gravitational force is always attractive in nature and the direction of the force is along the line joining the two masses.
M F M Figure . Attraction of two masses towards each other. In cartesian coordinates, the square of the distance is expressed as r x = ( y z . This is dealt in unit .
EXAMPLE . Consider two point masses m and m which are separated by a distance of meter as shown in the following figure. Calculate the force of attraction between them and draw the directions of forces on each of them. Take m = kg and m = kg m m m x y z Points to Contemplate DATA PROBLEM Planet a What is the law connecting a and T?
B C Comment on the relation between a and T for these imaginary planets . . Universal Law of Gravitation Even though Kepler’s laws were able to explain the planetary motion, they failed to explain the forces responsible for it. It was Isaac Newton who analyzed Kepler’s laws, Galileo’s observations and deduced the law of gravitation.
Newton’s law of gravitation states that a particle of mass M attracts any other particle of mass M in