Velocity of a Spacecraft

Question: How is acceleration the velocity of a spacecraft measured?
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Measuring the Doppler shift of emission lines in the light of
nearby stars would tell you your relative velocities to those stars.

John Hawley
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The previous answer does not seem like a practical method of 
measuring speeds
well.   Stars are not monochromatic sources that one can get an accurate
"Doppler shift" from.  Stars and galaxies are moving in all directions, so
there is no real fixed point of reference.

When people talk about measuring the acceleration or velocity of spacecraft,
they usually are referring to ordinary satellites and spacecraft in orbit
around Earth or on a planetary mission.

These spacecraft get velocity, position, and acceleration information by
sending and receiving radio signals from ground stations.  Using Doppler
shift, time delay, and very-long-baseline information, the position, speed,
and acceleration of a spacecraft can be measured very accurately, relative
to the earth.  The speed and position of the earth are known very accurately
too, and combining the information lets you know what your motion is in the
solar system.

If you are in your spacecraft flying around by yourself and want to know
your acceleration, you can use an on-board accelerometer.  These are very
accurate.  By keeping track of acceleration, you can determine your
velocity.  If you want to know absolute acceleration in the framework of the
universe, this will not work because the accelerometer will not sense the 
effect
of a nearby planet which you might be orbiting.  Your accelerometer will
read zero whether you are in free space or orbiting something.

On the other hand, if you are in your spacecraft flying around by yourself
and want to know where you are and how fast you are going, you can (in
theory) use optical methods.  By sighting on nearby planets and stars with
an accurate telescope, you can determine where you are.  Of course you need
a huge database of information that tells exactly where convenient stars and
planets are in space and time, and a way of triangulating yourself.

Bob Erck
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