This calc uses standard methods to take relativity into account while calculating the Doppler shift of electromagnetic radiation. The "object speed" is only the speed in the radial direction (i.e. away from the observer - use a negative value for travel towards the observer).
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This earth orbit calculator determines the speed and orbital period of a satellite at a given height above average Earth sea level.
Earth Orbit Calculator
The escape velocity calculator tells you how fast an object should move to escape the gravitational force of any celestial body.