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Question
What is the angular velocity of the Earth around the Sun? How do we get it?
Asked by: Zahi Assir
Answer
Calculating the angular velocity of the Earth is a deceptively easy task. The reason for
this is simple - the angular velocity is defined as the angle subtended in a certain time.
We know the Earth goes round the Sun, all the way around is 2 radians (360 degrees).
We also know that it takes a year (approx 365 days) which is therefore about 3.2x107 secs.
Therefore  = 2 / 3.2x107 = 2.0x10-7 rad/s. We have calculated the angular velocity.
However, if we can measure the distance to the Sun we can also calculate the velocity of
the Earth relative to the Sun. Although unless we define a direction this is more
technically known as the speed. This can be done by looking at the definition of the
radian. The radian is a unit which conects the radius of an arc, the length of the arc and
the angle subtended by the arc. The formula for this is s = r x  (where s is the
length of the arc, r is the radius and the angle). So if we know the radius of the
Earth's orbit (1.5x1011m) we can substitute the angular velocity from our previous equation
to give v = x r (where v is the velocity, the angular velocity and r the
radius).
So, the Earth travels through space (relative to the Sun) at:
v = 2.0x10-7 x 6.4x106 = 3.0x104m/s
Answered by: Edward Rayne, Physics Undergraduate Student, Cambridge UK
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