Satellites as Projectiles in Free Fall

Introduction

• Satellites in orbit around Earth exhibit a unique form of motion.
• Understanding how satellites behave as projectiles in free fall is essential for space science.

Satellites as Projectiles

• A satellite in orbit can be considered a projectile.
• It maintains a constant horizontal speed as it orbits Earth.
• Simultaneously, it is in free fall towards Earth due to gravity.
• This dual motion results in the satellite following a curved path known as an orbit.

Projectile Motion in Orbit

• When a satellite is launched into orbit, it is given an initial horizontal velocity.
• The satellite's inertia keeps it moving forward horizontally.
• Gravity continuously pulls the satellite toward Earth's centre.
• The combination of these forces results in the satellite's curved trajectory.

Key Concepts

• Constant Horizontal Speed: Satellites maintain a constant horizontal speed, allowing them to stay in orbit without falling directly to Earth's surface.
• Acceleration Due to Gravity: Despite their horizontal motion, satellites are affected by gravity, which causes them to fall toward Earth. However, their forward motion prevents them from crashing into Earth.
• Curved Trajectory: The combination of horizontal velocity and the downward force of gravity results in a curved trajectory, creating an orbit.

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Satellites as Projectiles in Free Fall

Formulas and Calculations

• The centripetal force required to keep a satellite in orbit is given by:
• F_centripetal = (m × v²)/r
  • F_centripetal: Centripetal force
  • m: Mass of the satellite
  • v: Velocity of the satellite
  • r: Radius of the satellite's orbit
• The gravitational force between Earth and the satellite is given by:
• F_gravity = (G × m_earth × m_satellite)/r²
  • F_gravity: Gravitational force
  • G: Universal gravitational constant
  • m_earth: Mass of Earth
  • m_satellite: Mass of the satellite
  • r: Distance between Earth's centre and the satellite