Answer:
a_c = 1.67 x 10⁻¹⁰ m/s²
Explanation:
given,
time period = 2.60 x 10⁸ yr
T = 2.60 x 10⁸ x 365 x 24 x 60 x 60
T = 8.2 x 10¹⁵ s
radius, R = 3.00 x 10⁴ light year
R = 3 x 10⁴ x 3 x 10⁸ x 365 x 60 x 60 x 24
R = 2.84 x 10²⁰ m
now, angular velocity of sun
[tex]\omega = \dfrac{2\pi}{T}[/tex]
[tex]\omega = \dfrac{2\pi}{8.2\times 10^{15}}[/tex]
ω = 7.68 x 10⁻¹⁶ rad/s
centripetal acceleration
a_c = r ω²
a_c = (2.84 x 10²⁰) x (7.68 x 10⁻¹⁶)²
a_c = 1.67 x 10⁻¹⁰ m/s²
centripetal acceleration of the Sun in its galactic orbit is equal to
1.67 x 10⁻¹⁰ m/s².
