Question

The radius of the earth's very nearly circular orbit around the sunis 1.5\times10^11 m. Find the magnitude of the earth's velocity as it travels around thesun. Assume a year of 365 days.
Express your answer using two significant figures. wherev=km/s
Find the magnitude of the earth's angular velocity as it travelsaround the sun. Assume a year of 365 days.
Express your answer using two significant figures. wherew=s^-1
Find the magnitude of the earth's centripetal acceleration as ittravels around the sun. Assume a year of 365 days.
Express your answer using two significant figures. wherea=m/s^2

Answer 1

A) Linear distance covered = circumference of orbit
Velocity = distance / time
Velocity = 2πr / T
Velocity = (2π x 1.5 x 10¹¹) / (365 days a year x 24 hours per day x 60 minutes per hour x 60 seconds per minute)
Velocity = 29,886 m/s
Velocity = 30 km/s

B) ω = 2π/T
ω = 2π / (365 x 24 x 60 x 60)
ω = 1.99 x 10⁻⁷ rad/s
ω = 2.0  x 10⁻⁷ rad/s

C) centripetal acceleration = v²/R
a = (30 x 10³)² / (1.5 x 10¹¹)
a = 6 x 10⁻³ m/s²