If the Milky Way and the Andromeda galaxies are approximately 2 million light years apart and are moving toward each other at 199 km/sec, how long will it take before the two galaxies collide?
To calculate the time it will take for the Milky Way and the Andromeda galaxies to collide, we need to find the distance between them and divide it by their relative velocity. Let's break it down step by step:
Step 1: Convert the relative velocity to the same units as the distance.
The relative velocity is given as 199 km/sec. We need to convert this to the same units as the distance, which is in light years. We can convert kilometers to light years by multiplying the velocity by the conversion factor.
1 light year = 9.461 × 10^12 km
So, the relative velocity in light years per second is calculated as:
199 km/sec × (1 light year / 9.461 × 10^12 km) = 2.105 × 10^-11 light years per second
Step 2: Divide the distance by the relative velocity.
The distance between the Milky Way and the Andromeda galaxies is given as 2 million light years. Now, divide this distance by the relative velocity in light years per second:
2 million light years / (2.105 x 10^-11 light years per second) = 9.51 × 10^20 seconds
Step 3: Convert seconds to a more meaningful unit of time.
9.51 × 10^20 seconds is not very convenient to understand, so let's convert it into a more meaningful unit, such as years. There are about 31,536,000 seconds in a year.
9.51 x 10^20 seconds / 31,536,000 seconds per year = 3.02 x 10^13 years
Therefore, it will take approximately 30.2 trillion years for the Milky Way and Andromeda galaxies to collide.
It's important to note that this estimated time scale assumes the current rates of motion will remain constant, and factors such as dark matter and the gravitational influence of other celestial objects can also impact the trajectory and timing of the collision.