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At orbit, gravitational force = centripetal force. mrɷ2 = GMm/r2

Where M is the mass of the planet, 'r' the distance from the center of the planet.

ɷ2 = GM/r3

And since ɷ = 2π/T,

(2π/T)2 = GM/r3

(T/2π)2 = r3/GM

T2 = 4π r3 / GM

T = √(4π r3 / GM)

Which is the required expression for time period.

HTH

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14y ago
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13y ago

Orbital velocity depends on the altitude of the orbit. From Low Earth Orbit (abbreviated LEO), orbital velocity is about 18,000 miles per hour. Higher orbits are at slower speeds.

Around any planet with an atmosphere, such as the Earth or Venus, there is a minimum altitude for a "stable" orbit; too low, and you'll slow down and fall because of atmospheric friction. That minimum altitude is about 120 miles up, although even at higher altitudes there is still some tiny bit of friction. In fact, the ISS occasionally needs to be boosted into a slightly higher orbit because the tiny air friction at that altitude is enough to slow it down!

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11y ago

Any speed = Distance/Time

Orbital speed = Distance around the full orbit/Period of revolution

For a circular orbit:

Speed = 2 x (pi) x Orbital radius/Period of revolution

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10y ago

The shift of the frequency spectrum of a sound or electromagnetic source

is an indicator of the radial component of its velocity relative to you.

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Q: How do you determine orbital velocity?
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