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The earth revolves around the sun in a circular path with a speed of 30km/s. What is the radial acceleration directed towards the sun

The earth revolves around the sun in a circular path with a speed of 30km/s. What is the radial acceleration directed towards the sun

Grade:11

2 Answers

Vikas TU
14149 Points
4 years ago
Dear student 
Speed of revolution = 30Km/s
                               = 3 x 10 ^4 m/s
Time of revolution = One year = 356 days (convert into seconds)
                            = 365 x 24 x 60 x 60 = 3.5 x 10 ^7 seconds
The formula of radial acceleration:
                     ac = V^2 / r
Distance covered by the earth around the sun will be equal to the circumference of orbit.
      Speed x Time ( V.T ) = 2πr
                               r = V.T/2π  
                      ac = V2 / r = V ^2 x 2π/V.T  
                              ac = 2πV /T
                              ac = 2 x 3.14 x 3 x 10 ^4/ 3.5 x 10 ^7  
                              ac = 5.98 x 10 ^-3 m/s2
 
Arun
25750 Points
4 years ago
Here, the Earth revolves around the sun in a circular path with a speed of 30 km per second
Speed of revolution = 30 km/s = 3 * 10⁴ m/s.
Time of revolution = 1 year = 365 * 24 * 60 * 60 = 3.15 * 10⁷ sec
=> Radial acceleration, a_c = v₂/ r
Distance covered by Earth = circumference of orbit
V.T = 2πr
r = V.T / 2π
∴ a_c = v² / r
= v² 2π / v T
= 2πV / T
= 2π * 3 * 10⁴ / 3.15 * 10⁷
= 5.98 * 10⁻³ m/s²
Thus, a radial acceleration directed towards the sun​ is 5.98 * 10⁻³ m/s²
 

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