Physics Gravitation

8.12

Mass of the Sun, $M_s$ = $2*{10}^{30}$ kg, Mass of the Earth, $M_e$ = $6*{10}^{24}$ kg

Orbital radius, r = $1.5*{10}^{11}$ m

Let the mass of the rocket be, m

Let x be the distance from the centre of the Earth where the gravitational force acting on satellite P becomes zero.

From Newton's law of gravitation, we can equate gravitational forces acting on the satellite P under the influence of the Sun and the Earth as:

$\frac{G_m{M}_s}{({r-x)}^2}$ = $G_m\frac{M_e}{x^2}$ or( ${\frac{r-x}{x})}^2$ 

= $\frac{M_s}{M_e}$( ${\frac{r-x}{x})}^2$ = $\frac{{2*10}^{30}}{{6*10}^{24}}$ ,

 $\frac{r-x}{x}$ = 577.35 , r = 578.35x ,

x = $\frac{1.5*{10}^{11}}{578.35}$ = 2.59 $*{10}^8$ m

Ans.8.1

(a) No. Unlike electrical forces, gravitational force is independent of the status of the objects.

(b) Yes, the size of the space station is large enough and the astronaut will detect the change in Earth's gravity.

(c) Tidal effect depends inversely upon the cube of the distance while gravitational force depends inversely on the square of the distance. Since the distance between the Moon and the Earth is smaller than the distance between the Sun and the Earth, the tidal effect of the Moon's pull is greater than the tidal effect of the Sun's pull.

When there is no normal force acting on a body, weightlessness is experienced, and the body free fall under gravity. The concept of gravity is still acting on the body, however, there is no weight sensation of any reaction force from any surface or ground. The weightlessness felt by the astronauts in an orbiting spacecraft is not because gravity is not present but because while they are moving forward, both, they and the spacecraft are in continuous free fall towards the Earth. The role of the normal force in defining weight can be understood from this phenomenon also how it is different from the actual gravitational force.

When there is no normal force acting on a body, weightlessness is experienced, and the body free fall under gravity. The concept of gravity is still acting on the body, however, there is no weight sensation of any reaction force from any surface or ground. The weightlessness felt by the astronauts in an orbiting spacecraft is not because gravity is not present but because while they are moving forward, both, they and the spacecraft are in continuous free fall towards the Earth. The role of the normal force in defining weight can be understood from this phenomenon also how it is different from the actual gravitational force.

The gravitational pull of the Moon is the main reason behind the tides of Earth and it is less dependent on the sun. The gravitational pull of the moon on Earth is stronger than the sun's gravitational pull due to Earth's proximity to the moon. The Earth's oceans get pulled by the moon's gravity, which creates a bulge of water on the side of the Earth facing the moon. Also, another bulge gets created on the opposite side due to the water's inertia. When the earth rotates, its areas pass through these bulges which form the high and low tides. Each day, two high and two low tides are created by the gravitational interaction.