Circular orbits under gravity, and satellites

 

Basic relationships between speed, radius, period, acceleration and force

Here is a demonstration of the relationships between orbital speed, radius, period, centripetal acceleration, and gravitational centripetal force for an object of mass m2 in orbit around an object of mass m1.

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Geostationary orbits

notes_page3Polar orbits

A polar orbit is one that goes over the top of each of the north and south poles.  They are often used for surveying: to understand why, it is worth looking at this video of a polar orbit in Kerbal Space Program or this one from EUMETSAT.

Not every circular polar orbit will cover the whole surface of a planet.  If you have a globe, or a good imagination, it is worth trying to work out what happens with polar orbits whose period is some exact multiple of the planet’s day.

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6 thoughts on “Circular orbits under gravity, and satellites

  1. Hello,
    I’m just wondering what were you trying to calculate when you did -d^2R/dt^2? Is that the total acceleration of m1 and m2?
    Thanks!

    1. Hi Claire, thanks for your question.

      Yes that is absolutely right. Another way of stating this is to think about the centre of gravity of m1 and m2, which lies on the line between them. The masses m1 and m2 are both accelerating towards this centre of gravity, and the value -d^2R/dt^2 is the sum of the accelerations of the two masses.

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