Newton's Law of Universal Gravitation

Preliminaries

Use the GRESA Method to solve problems.
Example problem: Fyang (52 kg) experiences a net force of 1678.22 N. Determine Fyang’s acceleration.

Who developed the 3 laws of motion? Isaac Newton or Galileo Galilei (Answer: Isaac Newton)
Which law states that acceleration is directly proportional to net force but inversely proportional to mass? 1st law or 2nd law (Answer: 2nd law)
Which law states that a moving object will continue moving, and an object at rest will remain at rest unless acted upon by an unbalanced force? 1st law or 3rd law (Answer: 1st law)
Which law states that for every action, there is an equal and opposite reaction? 2nd law or 3rd law (Answer: 3rd law)
Wearing a seatbelt is an application of which law? 1st law or 2nd law (Answer: 1st law)

Objectives:
- Explain Newton’s Law of Universal Gravitation.
- Explain why objects near Earth's surface fall with identical acceleration in the absence of air resistance.
- Solve word problems related to the universal law of gravitation.

Arrange the following from least to greatest:
- Inertia
- Weight
- Force exerted to another object

Previously defined as the push or pull of objects.
This definition is vague, as it only defines forces in touch with the object.
Today's focus: Gravitational Force, a force that doesn't require direct contact.

Contact Forces:
- Involve direct contact between two bodies (push or pull).
- Examples: Normal Force, Friction, Tension.
Non-Contact Forces:
- Act even when bodies are separated by empty space.
- Examples: Magnetic Force, Gravity.

Newton questioned why the apple fell straight down instead of sideways or upward.
He realized a force pulls objects toward Earth—gravity.

Newton's intuition was a revolutionary break from the Ancient Greeks' notion of separate Terrestrial and Cosmic/Celestial Laws.
Newtonian Synthesis is the union of these laws based on Newton's observations.

Isaac Newton revised his synthesis based on experiments and published Newton’s Law of Universal Gravitation.
Every point mass attracts every other point mass in the universe with a force pointing in a straight line between their centers of mass.
- This force is proportional to the masses of the objects and inversely proportional to the square of their separation.

Fg = G \frac{m1 m_2}{r^2}
- F_g = Gravitational force (N)
- G = Gravitational constant (6.674 x 10^{-11} N m^2/kg^2)
- m = Mass (kg)
- r = Distance between two masses (m)

Compute the gravitational force between the moon (7.34 x 10^{22} kg) and the earth (5.97 x 10^{24} kg) if their average separation is 3.83 x 10^8 meters.
Given:
- m_1 = 7.34 x 10^{22} kg
- m_2 = 5.97 x 10^{24} kg
- r = 3.83 x 10^8 m
- G = 6.674 x 10^{-11} N m^2/kg^2
Required: F_g
Equation: Fg = G \frac{m1 m_2}{r^2}
Solution:
- F_g = (6.674 x 10^{-11}) \frac{(7.34 x 10^{22})(5.97 x 10^{24})}{(3.83 x 10^8)^2}
Answer:
- F_g = 1.99 x 10^{20} N

Determine the gravitational force between the Earth (m = 5.97 x 10^{24} kg) and a 70-kg physics student in an airplane at 40000 feet above Earth's surface (distance of 6.39 x 10^6 m from Earth's center).
Given:
- m_1 = 5.97 x 10^{24} kg
- m_2 = 70 kg
- r = 6.39 x 10^6 m
- G = 6.674 x 10^{-11} N m^2/kg^2
Required: F_g
Equation: Fg = G \frac{m1 m_2}{r^2}
Solution:
- F_g = (6.674 x 10^{-11}) \frac{(5.97 x 10^{24})(70)}{(6.39 x 10^6)^2}
Answer:
- F_g = 683.06 N

The mass of one small sphere in a Cavendish balance is 0.0100 kg, the nearest large sphere is 0.500 kg, and the center-to-center distance is 0.0500 m. Find the gravitational force on each sphere.
Given:
- m_1 = 0.0100 kg
- m_2 = 0.500 kg
- r = 0.0500 m
- G = 6.674 x 10^{-11} N m^2/kg^2
Required: F_g
Equation: Fg = G \frac{m1 m_2}{r^2}
Solution:
- F_g = (6.674 x 10^{-11}) \frac{(0.0100)(0.500)}{(0.0500)^2}
Answer:
- F_g = 1.33 x 10^{-10} N

Artificial satellites are useful in collecting data from Earth.
Satellites are attracted to Earth and vice versa because of gravitational force.