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1.6.2Dynamics

Projectile Motion and Satellites

5 min read 5 parts Lesson 22 of 22

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Section 1 of 5Newton’s Thought Experiment

1.6.2 Projectile Motion and Satellites

A satellite is not floating free of gravity; it is a projectile that keeps falling around the planet.

Cannon on a mountain
  • Imagine a cannon at the top of a high mountain firing a ball horizontally, with no air resistance.
Low speed
  • At a low speed the ball follows a curve and lands near the mountain, like any projectile.
Higher speed
  • The faster the ball is fired, the further it lands because the Earth's surface curves away beneath it.
Orbit
  • At a high enough speed the ball falls towards the Earth but the surface curves away at the same rate, so it never lands.

Section 2 of 5Gravity and Orbits

Gravity and Orbits
Force
  • Gravity is the unbalanced force acting on the satellite, pulling it towards the centre of the Earth.
Direction change
  • This force keeps changing the direction of the velocity, so the satellite follows a circular path.
Speed
  • The speed of the satellite is nearly constant, but its velocity is changing because its direction is changing.
Altitude
  • Lower orbits need a higher speed and have shorter periods than orbits further from the Earth.
Launch speedResult
LowFalls to ground as a projectile
HigherLands further away
Orbital speedOrbits the Earth

Section 3 of 5Link to Projectile Motion

1
A projectile has a constant horizontal velocity and a downward acceleration caused by gravity.
2
A satellite also has a sideways velocity, and gravity is the force producing its acceleration towards the Earth.
3
The sideways motion carries the satellite round the curve of the Earth as quickly as gravity pulls it down.
4
Because there is almost no air at orbital height there is no friction to slow it, so the orbit continues for years.
5
Astronauts in orbit seem weightless because they and the spacecraft are falling together.

Section 4 of 5Worked Example

Question

  • A satellite travels at 7500 m/s.
  • How far does it move along its orbit in 60 s?
  • Explain why it does not fall to the ground.

  1. Distance = v t = 7500 × 60.
  2. Distance = 450 000 m = 450 km.
  3. It does fall towards the Earth, but its sideways speed carries it forward so that the surface curves away beneath it as quickly as it falls.

Answer

  • 450 km along its orbit;
    • the satellite is continually falling around the Earth.

Section 5 of 5Exam Checklist & Tips

1.6.2 – Key Points for the Exam

  • Satellite An object that orbits a planet or star.
  • Orbit The curved path of an object around a planet or star under gravity.
  • Gravity The attractive force between objects with mass.
  • Tangential velocity Velocity directed along the edge of the circle, at right angles to the radius.

Common Mistakes

  • Saying there is no gravity in orbit; gravity is what keeps the satellite there.
  • Believing the satellite is not falling.
  • Thinking a satellite moves in a circle because of a force pushing it forward.
  • Assuming astronauts are weightless because they are outside Earth's gravity.
Physics 0625 & 9702 SUVAT Mastery Graph Interpretation

Constant Acceleration Equations (SUVAT) & Slopes

v = u + at  |  s = ut + ½at2  |  v2 = u2 + 2as  |  s = ½(u + v)t

  • Displacement-Time Graph: Gradient = Velocity (curve = accelerating).
  • Velocity-Time Graph: Gradient = Acceleration; Area under curve = Distance travelled / Displacement.
  • Free Fall in vacuum: a = g ≈ 9.81 m/s2 downwards (air resistance negligible).