# unit 4 section 2 orbits

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## orbits - period and speed

F = mv^2/r             +             F = GMm/r^2

V = squareroot(GM/r) - so speed is inversely proportional to the squareroot of the radius = V < 1/squareroot(r)

v = 2PIEr/T

T = 2PIEr/v

Finally;

T = 2PIEr/v

T = 2PIEr/squareroot(GM/r)

T = 2PIErsquareroot(r)/squareroot(GM)

T = squareroot(4PIE^2r^3/GM)

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## kinetic and potential energy of satellites

a satellites total enrgy and total kinetic and potential energy is constant

in a circular orbit its speed and distance above the mass its orbiting is constant

an elliptical orbit, a satellite will speed up as its height decreases and slows down as its height increases.

its kinetic energy increases as its potential energy decreases and vice versa, so the total energy remains constant.

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## geosynchronous satellites

geosynchronous satellites orbit the earth and have an orbital period equal to the rotational period of the earth

these satellites are really useful sending communications signals.

they return to the same position in the sky approximately every 24 hours.

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