Determine the acceleration of earth due to its motion around the sun. assume the earth's orbit to be circular with a radius of 1.5 x 10^8 km.

The definition of centripetal acceleration allows to find the result for the acceleration of the earth around the sun is:

          a = 5.95 10⁻³ m / s²

Centripetal acceleration is the acceleration of a body where all the energy is used to change the direction of the velocity keeping the value of its modulus constant.

They indicate that the radius of the circular orbit is r = 1.5 10⁸ km = 1.5 10¹¹m.

In a circular motion the speed is constant, therefore we can use the uniform motion relation to find the speed.

The length of the orbital circle is:

           L = 2π r

The time for a complete orbit is called the period.

          v =  

The period of the Earth's orbit is one year.

        T = 1 year (365 days / 1 year) (24 h / 1 day) (3600 s = 1 h)

        T = 3.154 10⁷ s

Let's calculate the velocity.

         v = 2 pi 1.5 1011 / 3.154 10⁷

         v = 2.988 10⁴ m / s

Now we can calculate the acceleration.

        a = 5.95 10⁻³ m / s²

In conclusion using the definition of centripetal acceleration we can find the result for the acceleration of the earth around the sun is:

          a = 5.95 10⁻³ m / s²

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Explanation:

Given

Radius of orbit

As earth moves around sun it experiences a centripetal force on it which is given by

where v=velocity of earth

Time period of Revolution

time period is 365 days i.e.

acceleration due to gravity is

is less than gravity

v=ir = 3x15 =45 v