Newton's Law of Gravitation

Newton's Law of Gravitation

• The formula for gravitational attraction between two point masses is F = Gm₁m₂ / r², where G is the gravitational constant.
• The force is directed along the line connecting the two masses, highlighting the nature of the interaction.
• This force is a conservative force field, implying that mechanical energy remains constant throughout the motion.
• It functions as a central force field, which ensures the conservation of angular momentum during an interaction.

Gravitational Field Due to Spherical Shell

• The gravitational field outside a spherical shell is given by E = GM / r², applicable for r > R, where R is the radius of the shell.
• At the surface of the shell (r = R), the gravitational field is expressed as E = GM / R².
• Inside the shell (r < R), the gravitational field is zero, indicating no gravitational influence within the shell.
• The direction of the gravitational field is always directed towards the center of the shell.

Gravitational Field Due to Solid Sphere

• The gravitational field outside a solid sphere is determined by E = GM / r², for r > R.
• At the surface of the sphere, the field is E = GM / R².
• For points inside the sphere (r < R), the gravitational field varies linearly with distance from the center, given by E = GMr / R³.

Acceleration Due to Gravity

• The acceleration due to gravity near the surface of a celestial body is expressed as g = GM / R².
• At a height h above the surface, the acceleration due to gravity can be calculated with the formula gh = GM / (R + h)².
• As height increases, the acceleration due to gravity decreases following the inverse square law principle.

Test your understanding of Newton's Law of Gravitation and the gravitational field of spherical shells. This quiz covers the formula for gravitational attraction, properties of conservative force fields, and behavior of gravitational fields outside and inside a spherical shell. Challenge yourself to deepen your knowledge of these fundamental concepts in physics.