Centripetal Force and Circular Motion

Study Notes

Centripetal force is a force that makes a body follow a curved path.
Its direction is always orthogonal to the motion of the body and towards the fixed point of the instantaneous center of curvature of the path.
To make a body follow a curved path, the centripetal and gravitational forces should be the same and balance with the speed of the body.

Find the speed of a satellite moving in a circular orbit at a height of 3800 km above the surface of the earth.
Given: mass of the earth (M) = 5.97 x 10^24 kg, radius of the earth (R) = 6.38 x 10^6 m
Solution: v = 6254.3 m/s, period (T) = 10227 s ≈ 2.84 hours

Gravity is the force that pulls you down or holds you in place.
Gravity at any point on the earth is the vectorial resultant of the gravitational force (F) and centrifugal force (Fc).
In simplified form: g = F + Fc = (G M m) / R^2 + ω^2 R cos φ

Gravity at the pole is stronger than at the equator due to the centrifugal effect.
The centrifugal force is maximum at the equator and minimum at the pole.

Physical Geodesy is the study of the physical properties of the gravity field of the earth, with a view to their application in geodesy.
Includes:
- Geoid undulation
- Gravimetric deflection
- Earth's shape and size (semi major, semi minor, and flattening)

Gravity is the force that pulls you down or holds you in place.
It is the vector force of attraction that exists between all particles with mass in the universe (Newton's 3rd Law).
Responsible for holding objects onto the surface of planets and keeping objects in orbit around another.

Newton's 1st Law (Law of Inertia):
- Every object persists in its state of rest or uniform motion, unless it is compelled to change that state by a force impressed on it.
Newton's 2nd Law:
- The time rate of change in momentum is proportional to the applied force and takes place in the direction of the force.
- F = ma, where F = force, m = mass, and a = acceleration.
Newton's 3rd Law:
- Whenever one body exerts force upon a second body, the second body exerts an equal and opposite force upon the first body.

Based on Newton's 3rd Law:
- "Every object in the Universe attracts every other object with a force directed along the line of centers for the two objects that is proportional to the product of their masses and inversely proportional to the square of the separation between the two objects."
F = Gravitational force between two objects
m1, m2 = Mass of 1st and 2nd objects
r = Distance between the objects
G = 6.674215 x 10^-11 Nm^2kg^-2

Based on Newton's 2nd and 3rd Laws:
- F = ma or F = mg
- g = GM / r^2
Gravitational field strength generated by the earth at the surface:
- M = 9.8 x (6.37 x 10^6)^2 / (6.67 x 10^-11) = 5.96182 x 10^24 kg

Centripetal force:
- A force that makes a body follow a curved path.
- Balanced by a reaction force known as centrifugal force.
Centrifugal force:
- Not a force but the experience of an inertial force experienced in a rotating reference frame acting away from the center of rotation.
- Directed outward and is perpendicular to the rotation axis.