Newton's gravitational force: ( F = \frac{G m_1 m_2}{r^2} )
Features:
Central and conservative force
Long range
Follows inverse square law
Always attractive
Medium independence
Gravitational Field Intensity
Divide gravitational force by mass: ( g = \frac{F}{m} )
Unit: Newton/kilogram (N/kg)
Why it's always inward
Gravitational Force and Radius
If two objects are ( m_1 ) and ( m_2 ), their gravitational force depends on ( F = \frac{G m_1 m_2}{d^2} ), where ( d ) is the distance between their centers.
If using ( r ), then ( F = \frac{G m_1 m_2}{(2r)^2} ).
Specific Gravity
Specific gravity or relative density does not depend on gravitational force in the medium.
Effect of Height on Gravitational Field
At height, gravitational field is inversely proportional to distance.
While going down, gravitational field is directly proportional to distance.
Gravitational formula: ( g = g_0(1 - \frac{2h}{R}) ), ( h ) should be small.
Potential Energy and Escape Velocity
Potential energy: ( U = -\frac{G m_1 m_2}{r} )
Escape velocity: ( v_e = \sqrt{\frac{2GM}{R}} )
Satellite and Conservation of Energy
Angular momentum of a satellite in a circular orbit remains conserved.
Relationship between kinetic energy and potential energy -
Kinetic energy = ( -\frac{1}{2} ) potential energy.
Other Important Points
If the direction of gravitational force is negative, it will always be attractive.
Graph of gravitational field intensity vs. distance will not be positive.
At the exact center, gravitational field is zero.
Questions and Answers
Question: What happens to gravity when we go above the Earth's surface?
Answer: Gravity decreases when going above.
Question: Is the gravitational field always attractive?
Answer: Yes, the gravitational field is always attractive.