Chapter 4: Gravity, Projectiles, and Satellites Overview
Concepts covered in the lecture:
Universal Law of Gravity
Inverse-Square Law: Gravity and Distance
Weight and Weightlessness
Universal Gravitation
Projectile Motion
Fast-Moving Projectiles—Satellites
Circular Satellite Orbits
Elliptical Orbits
Escape Speed
Newton's Law of Universal GravitationEvery body in the universe attracts every other body with a force that:
Is directly proportional to the product of their masses.
Is inversely proportional to the square of the distance between their centers:Formula: F = G (m1 × m2) / d²
The force required increases with mass and decreases with the square of distance. Earth's surface exerts a force of 9.8 N on a 1-kg mass.
Inverse-Square LawDefinition: The law states that the intensity of any effect—such as gravitational force—varies inversely with the square of the distance from its source.As distance from the Earth increases, the gravitational force felt by an object decreases rapidly, approaching zero but never actually reaching it. If you double the distance from the Earth, the gravitational force experienced is only one-fourth as strong because it is divided by the square of the distance ( (2²=4). This principle also applies to various phenomena beyond gravity, including:
Electric Fields: The intensity of electric forces from a charge diminishes with the square of the distance between the charge and a point.
Light Intensity: The brightness of light decreases as you move away from the source according to the inverse-square law.
Radiation: The intensity of radiation also follows this principle—higher distance results in considerably lower exposure levels.
Sound Intensity: Although sound behaves differently in some contexts, in free space, sound intensity decreases as it travels due to the dispersion over a larger area.
Weight and Weightlessness
Weight Definition: The gravitational force exerted on an object by the nearest massive body (e.g., Earth).
Weightlessness: Occurs when there is no support force acting on a body, as experienced during free fall or in a free-falling elevator
Examples of Weight and Weightlessness: An astronaut feels weightless when in free fall as all support forces are absent.
Projectile MotionDefined as any object moving through the air or space under the influence of gravity, following a curved (parabolic) path. Motion consists of:
Key points about projectile motion:
Vertical velocity changes over time, while horizontal velocity remains constant.
Distance fallen after time 't' can be calculated with: d = ½ gt².
Fast-Moving Projectiles
Satellites: A projectile must move at sufficient horizontal speed to fall continually around Earth without hitting it—essentially orbiting. To maintain orbit, a projectile must achieve a horizontal velocity of approximately 8 km/s.In orbit, the path of the projectile matches the curvature of Earth.
Circular and Elliptical Orbits
Circular Orbits: Requires constant speed (8 km/s) and a constant distance from the center of Earth. No component of force acts in the direction of motion—only direction changes.
Elliptical Orbits: Speed and distance from Earth vary. High speed allows a satellite to overshoot and then regain speed closer to Earth. Comets follow highly eccentric elliptical paths around the sun.
Escape Speed: Defined as the minimum speed needed to break free from Earth's gravitational influence. The escape speed is about 11.2 km/s. The formula for escape speed from any celestial body is: V = √(2GM/d).
Key Terms
Projectile: Object influenced by gravity in motion.
Parabola: The curved path followed by a projectile under gravity.
Satellite: A small celestial body that orbits a larger body.
Ellipse: An oval path taken by a satellite.
Escape Speed: The required speed to escape a celestial body's gravitational pull.
Weightlessness: A condition where no support force is felt.
Knowt
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