Find the acceleration of our galaxy, due to the nearest comparably sized galaxy. The approximate masses of each galaxy is 8 10¹¹ solar mass and they are separated by 2 million light-years. Each galaxy has a diameter of 100000 light year. (Assume, 1 light year 10¹⁶ ~m , gravitational constant, G 10⁻¹⁰ ( Nm ^2 ~kg ^2 ) and mass of sun =2.0 10³⁰ ~kg )

Step-by-step solution

Here, masses of each galaxy are aligned m₁ & =m₂=8 10¹¹ solar mass & =8 10¹¹ 2 10³⁰ ~kg & =16 10⁴¹ ~kg aligned Distance between galaxies is aligned d & =2 10^6 light year & =2 10^6 10¹⁶ ~m =2 10²² ~m aligned Force of gravitational pull on each of galaxy is F= G m₁ m₂ d^2 = 10⁻¹⁰ (16 10⁴¹ )^2 (2 10²² )^2 Acceleration of galaxy is aligned a & = F m = 10⁻¹⁰ (16 10⁴¹ )^2 (2 10²² )^2 16 10⁴¹ & = 10⁻¹⁰ 16 10⁴¹ (2 10²² )^2 =4 10⁻¹³ ~ms ⁻² aligned