3.5 Motions of Satellites and Spacecraft

Sending Objects into Orbit

• Object is launched with a velocity of v_a → a is where the object will strike the ground 

  • At higher velocities, the speed will carry it further before it hits the ground

Circular Satellite Velocity

• At a high enough velocity (with no air resistance) the curved surface of earth causes the ground to remain the same distance from the bullet 

  • It starts to fall at the same rate the earth curves

  • Approx 8km/s

    • Apogee: Earth’s satellites are the farthest from Earth 

    • Perigee: Earth’s satellite is the closest using the minimum velocity 

Centripetal Force

• The force needed to keep an object moving in a circle at a specific separation ® from the centre 

  • If gravitational force is equal to the centripetal force the orbit is circular 

  • Larger velocity: Stronger centripetal force than gravitational force 

    • Causes a wider swing and a curve away from the center 

  • Lower Velocity: Weaker centripetal force than the gravitational pull 

    • The path will curve inwards as it tries to gain energy 

Satellites decay

• At a certain point the atmospheres drag will lead to the satellite losing energy and causing it to lose its orbit 

Escape speed

• The speed needed to move away from the Earth forever 

  • Approx 11km/s

  • Spacecrafts: After escaping earth they enter an orbit around the sun with small trajectory adjustments from thruster rockets

Gravity Assist

•  The path of the spacecraft changes as it nears a planet due to its gravity 

Orbit around another planet

• Spacecraft must slow down so it can fall into the gravity of the planet 

  • To land: Slow down more

  • Return trip: Enough fuel to redo the whole process in reverse