#AP Physics 1: Gravitational Fields - Your Last-Minute Guide 🚀

Hey there! Let's make sure you're feeling awesome about gravitational fields for your AP Physics 1 exam. This guide is designed to be super clear, quick to review, and totally focused on what you need to know. Let's get started!

#1. Gravitational Force and Fields

#1.1. What is Gravitational Force?

• Definition: The force of attraction between any two objects with mass.
• Direction: Always acts vertically downwards, towards the center of the planet or celestial body. ⬇️
• Magnitude: Given by $F = mg$, where:
  • $F$ is the gravitational force (weight).
  • $m$ is the mass of the object.
  • $g$ is the gravitational field strength (acceleration due to gravity).

#1.2. Free Fall

• Definition: When the only force acting on an object is gravity. 🪂
• Acceleration: In free fall, the object's acceleration is equal to the gravitational field strength ($g$).
• Key Idea: All objects in free fall near the Earth's surface accelerate at approximately 9.8 m/s², regardless of their mass (ignoring air resistance).

#1.3. Gravitational Field (g)

• Definition: A region of space where a mass experiences a gravitational force. It's a vector field, meaning it has both magnitude and direction.
• Source: Created by any object with mass. The more massive the object, the stronger the field it creates.
• Direction: Points towards the center of the object creating the field.

#2. Calculating Gravitational Field Strength

#2.1. Newton's Law of Universal Gravitation

• Formula: $F = G \frac{m_1 m_2}{r^2}$, where:
  • $F$ is the gravitational force between two masses.
  • $G$ is the universal gravitational constant (6.67 \times 10^{-11} Nm^2/kg^2).
  • $m_1$ and $m_2$ are the masses of the two objects.
  • $r$ is the distance between the centers of the two masses.

#2.2. Deriving the Gravitational Field Equation

• Starting Point: Newton's Second Law ($F = ma$) and Newton's Law of Universal Gravitation.
• Orbital Scenario: Consider a satellite orbiting a planet. The gravitational force is the only force acting on the satellite, causing its centripetal acceleration.

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