🌍 Earth can be like a clingy ex; it doesn't want you to leave! So if we want to send satellites or spacecrafts far, we have to overcome its gravitational pull. Here's how it's done!

• Escape Velocity
  • What? - The speed an object must reach to break free from a celestial body's gravitational pull.
  • For Earth? - About 11,200 m/s (that's 40,000 km/h!).
• Total (Mechanical) Energy
  • Made up of gravitational potential energy + kinetic energy.
  • Golden Rule: For a spacecraft to reach infinity and escape Earth, its gravitational potential energy + kinetic energy = 0.
• Important Equations
  • Escape Speed: \(v_ese = \sqrt \frac {2GM}{r}\)
  • Relation with Orbital Speed: v_esc ​= v_orb​ × \(\sqrt2\)
  • Relating Escape Speed & Gravitational Field Strength - vesc ​= \(\sqrt2gr​\)

Fun Fact

• Escape velocity doesn't care about the satellite's mass! It just depends on the planet's properties.

• Moon Escape
  • Wanna leave the Moon? Your speed should be about 2.37 × 10³ m/s.
• Space Probe Math
  • Probe's mass: 2500kg.
  • Parking 350km above Earth.
  • It needs a "boost" in speed to truly escape.
  • Engine Work Done :7.4 x 10¹⁰ J.