The radius of the earth’s very nearly circular orbit around the sun is 1.5×1011m.

The radius of the earth’s very nearly circular orbit around the sun is 1.50×10 11 m. What is the magnitude of the earth‘s velocity and centripetal acceleration as it travels around the sun?

Answer:

Consider that in one year the Earth travels the entire circumference of the circle (ok, it should be an ellipse but let us assume it is a circle) of radius r=1.5×1011m
So :
in 1 year, 363 days, each day 24 hours, each hour 60 minutes and each minute 60 seconds, or:
365×24×60×60=3.15×107m≈3×107seconds.

Describing a distance of 2πr2.314.1.5×10111=9.42×1011m≈9×1011m

Velocity will be:  v=timedistance​=3×1079×1011​=3×104sm​

Centripetal acceleration will be ac​=rv2​=1.5×1011(3×104)2​=6×10−3s2m

​The radius of the earth’s very nearly circular orbit around the sun is 1.5×1011m.

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