Artificial satellites and weightlessness

Physics · Circular motion. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

A satellite stays in orbit because gravity provides the centripetal force it needs. This fixes the orbital velocity for each orbit radius. The speed does not depend on the mass of the satellite, and it is smaller in a larger orbit.

Your real weight is the pull of gravity, mg. Your apparent weight is the force a scale or floor exerts on you. In a lift accelerating upwards it is more than mg, and accelerating downwards it is less. In free fall, or in orbit, you and the floor fall together, so the contact force is zero. This is weightlessness, even though gravity still acts.

A geostationary satellite takes 24 hours to orbit above the equator, so it stays over one place on the Earth.

Rules to remember

Common mistake

Do not say there is no gravity in orbit. Gravity is the centripetal force that keeps the satellite in orbit; the astronaut feels weightless only because there is no contact force.

Worked example

A 60 kg man stands on a weighing machine in a lift that accelerates upwards at 2.0 m s−2. What does the machine read?

  1. Real weight = mg = 60 × 9.8 = 588 N.
  2. Accelerating upwards, the reading R is larger than the weight: R − mg = ma, so R = m(g + a).
  3. R = 60 × (9.8 + 2.0) = 60 × 11.8 = 708 N.

Answer: 708 N

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