3D Sun's Diameter Calculation
Example: Determining the Sun's Size in 3D
Class 11 Example 2.4 Simulation: Determine the Sun's physical diameter from its 1920' angular size and 1.496×10¹¹ m distance. Astronomy problem-solving practice.We can calculate the Sun's actual diameter using its angular size and distance from Earth:
- Angular diameter: 1920 arcseconds (about 0.53 degrees)
- Earth-Sun distance (D): 1.496 × 10¹¹ meters
What is the actual diameter of the Sun?
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Step-by-Step Solution
1
Convert angular diameter from arcseconds to radians:
1920" × (4.85 × 10⁻⁶ rad/1") = 9.31 × 10⁻³ radians
1 arcsecond = 1/3600 degree = 4.85 × 10⁻⁶ radians
2
We know the Earth-Sun distance:
D = 1.496 × 10¹¹ meters (1 astronomical unit)
3
Use the small angle formula to calculate diameter:
d = α × D
Where:
d = linear diameter
α = angular diameter (in radians)
D = distance to object
4
Plug in the values:
d = (9.31 × 10⁻³ rad) × (1.496 × 10¹¹ m) = 1.39 × 10⁹ meters
The Sun's diameter is approximately 1.39 million kilometers
(which is about 109 times Earth's diameter)
(which is about 109 times Earth's diameter)
Key Astronomical Concepts
Angular Diameter
The apparent size of an object as seen from Earth, measured as an angle. Even large objects appear small when very distant.
Small Angle Formula
For small angles (when the angle is less than a few degrees), we can approximate the relationship between an object's actual size, its distance, and its angular size with the simple formula: d = α × D.
Astronomical Scale
The Sun is enormous (1.39 million km diameter) but appears small (about 0.5°) in our sky because it's about 150 million km away. This demonstrates the vast distances in space.
