The earth travels around the sun once a year in an approximately circular orbit whose radius is 1.50x10^11 m. From this data determine (a) the orbital speed of the earth and (b) the mass of the sun.

(a) Determine the circumference of the Earth through the equation,

C = 2πr

Substituting the known values,

C = 2π (1.50 x 10¹¹ m)

C = 9.424 x 10¹¹ m

Then, divide the answer by time which is given to a year which is equal to 31536000 s.

orbital speed = (9.424 x 10¹¹ m) / 31536000 s

orbital speed = 29883.307 m/s

Hence, the orbital speed of the Earth is ~29883.307 m/s.

(b) The mass of the sun is ~1.9891 x 10³⁰ kg.