Luminosity, apparent brightness and distance

Answer

The **total power** the star radiates in all directions (in watts, W). It is a property of the star itself and does **not** depend on distance.

Answer

The power we **receive per square metre** at Earth (in W m⁻²). It **depends on distance** — the same star looks dimmer farther away.

Answer

$b = \dfrac{L}{4\pi d^{2}}$ — the inverse-square law (given in the data booklet).

Answer

By distance d the light has spread over a **sphere** of radius d, whose surface area is 4π d². The power L is shared over that area.

Answer

The apparent brightness falls to a **quarter** (1/2² = 1/4): twice as far → 4× the area → ¼ the brightness.

Answer

The tiny apparent **shift** of a nearby star against distant background stars as Earth orbits the Sun. A bigger shift means a closer star.

Answer

$d\,(\text{parsec}) = \dfrac{1}{p\,(\text{arc-second})}$ — distance in parsecs is one over the parallax angle in arc-seconds.

Answer

The distance at which a star shows a parallax angle of exactly **1 arc-second**. 1 pc ≈ 3.26 light-years ≈ 3.1 × 10¹⁶ m.

Answer

d = 1/p = 1/0.020 = **50 parsec**.

Answer

Equal b ⇒ d ∝ √L, so √100 = **10 times farther** away.

Answer

Only its **apparent brightness** (it drops as 1/d²). The **luminosity is unchanged** — that's a fixed property of the star.