Answer :
The acceleration of the earth around the sun is 5.95 103 m/s2, which is the definition of centripetal acceleration.
Definition of Centripetal Acceleration
A motion feature that applies to objects moving in a circular motion is called centripetal acceleration. It is referred to as moving with centripetal acceleration when an item moves in a circle including its acceleration vector pointing inside the direction of the circle's center.
The following is the result for the acceleration of the earth around the sun according to the definition of centripetal acceleration:
a = 5.95 10⁻³ m / s²
A body accelerates centripetally when all of its energy is put toward changing the direction of its velocity while maintaining a constant value for its modulus.
a= [tex]\frac{v^{2} }{r}[/tex]
They show that the circular orbit's radius is r = 1.5 10⁸ km = 1.5 10¹¹m.
Since the speed is constant in a circular motion, we may use the uniform motion relation to calculate the speed.
[tex]v = \frac{L}{t}[/tex]
The orbital circle has the following radius:
L = 2π r
The period is the amount of time required for an orbit to complete.
v = 2πr / t
The Earth's orbit has a year-long period.
T = 3.154 10⁷ s
Now let's determine the velocity.
v = 2 pi X 1.5 X [tex]10^{11}[/tex] / 3.154 10⁷
v = 2.988 10⁴ m / s
We can now determine the acceleration.
a= [tex]\frac{(2.988 X 10^{4} )}{1.5 X 10^{11} } ^{2}[/tex]
a = 5.95 10⁻³ m / s²
Using the definition of centripetal acceleration as a guide, we can conclude that the acceleration of the earth's rotation around the sun is as follows:
a = 5.95 10⁻³ m / s²
Learn more about Centripetal acceleration: https://brainly.com/question/14402637
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The complete question is:
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.
