Understanding the Concepts

* Angular diameter: The apparent size of an object as seen from a specific distance, measured in arcseconds.

* Linear diameter: The actual physical size of the object, measured in meters (or other units).

* Distance: The separation between the observer and the object.

Formula

The relationship between these three is:

```

Distance = (Linear Diameter) / (Angular Diameter in radians)

```

Conversion

* Arcseconds to radians: 1 arcsecond = (π / 180 / 60 / 60) radians ≈ 4.8481 × 10^-6 radians

Calculation

1. Convert angular diameter to radians: 100 arcseconds * (4.8481 × 10^-6 radians/arcsecond) ≈ 4.8481 × 10^-4 radians

2. Calculate the distance:

Distance = 30 meters / (4.8481 × 10^-4 radians) ≈ 61,959 meters

Answer

The object is approximately 61,959 meters (or about 62 kilometers) away.