The great galaxy in Andromeda has an angular diameter along its long axis of about 5 degree. Its distance is about 2.2 millons light years. What is its linear diameter.
Convert 5 degrees to radians (about 0.09) and multiply that by the distance from Earth. That will give you the diameter.
It's a big one, like our Milky Way.
Is this answer correct
.09 * 2.2 = .198
To calculate the linear diameter of the great galaxy in Andromeda, we can use the small angle formula.
The small angle formula relates the apparent size (angular diameter) of an object to its actual size (linear diameter) and the distance to the object. It can be represented as:
angular diameter = linear diameter / distance
Rearranging the formula, we have:
linear diameter = angular diameter * distance
Given:
Angular diameter = 5 degrees
Distance = 2.2 million light years
We need to convert the distance from light years to a more suitable unit, such as parsecs, before proceeding with the calculations. Since 1 parsec is approximately 3.26 light years, we can calculate:
Distance (in parsecs) = Distance (in light years) / 3.26
So, Distance (in parsecs) = 2.2 million light years / 3.26
Now, let's calculate the linear diameter:
linear diameter = 5 degrees * Distance (in parsecs)
Substituting the values we have:
linear diameter = 5 * (2.2 million light years / 3.26)
Calculating the above expression:
linear diameter ≈ 15,337.4 light years
Therefore, the linear diameter of the great galaxy in Andromeda is approximately 15,337.4 light years.
To find the linear diameter of the Andromeda galaxy, we can use the concept of angular diameter and trigonometry. The angular diameter is the angle subtended by an object, in this case, the Andromeda galaxy, as seen from a particular location (in our case, Earth). Here's how we can calculate the linear diameter:
1. Convert the angular diameter to radians: Since the angular diameter is given in degrees, we need to convert it to radians by using the formula:
Angular diameter in radians = (Angular diameter in degrees) x (pi / 180)
In this case: Angular diameter in radians = 5 degrees x (pi / 180)
2. Calculate the linear diameter using trigonometry: We can use the small-angle approximation, which assumes that for small angles, the tangent of the angle is approximately equal to the angle itself. The formula is:
Linear diameter = (Distance to the object) x (Angular diameter in radians)
In this case, the distance to the Andromeda galaxy is 2.2 million light-years. However, it's important to note that the speed of light is 299,792,458 meters per second. So let's convert the distance to meters:
Distance = 2.2 million light-years x (9.461 x 10^15 meters per light-year)
Now we can calculate the linear diameter:
Linear diameter = (Distance) x (Angular diameter in radians)
By substituting the calculated values, we can find the linear diameter of the Andromeda galaxy.