A-level Physics (Advancing Physics)/Large Units

The distances in space are so large that we need some very large units to describe them with.

Light Years
A light year is the distance that light travels in one year. The velocity of light is constant (3 x 108ms−1), so 1 light year is:

$$3 \times 10^8 \times 365.24 \times 24 \times 60 \times 60 \approx 9.46 \times 10^{15}\mbox{ m} $$

Light seconds, light minutes, light hours and light days are less commonly used, but may be calculated in a similar fashion.

Astronomical Units
1 astronomical unit (denoted AU) is the mean average distance from the Earth to the Sun. This is approximately 150 x 109m.

Parsecs
Degrees can be divided into minutes and seconds. There are 60 minutes in a degree, and 60 seconds in a minute. This means that 1 second is 1/3600 of a degree. A degree is denoted °, a minute ' and a second ". The definition of a parsec uses a simplified form of triangulation. It assumes that the perpendicular to the plane of the Earth's orbit passes through the Sun and a celestial object. A parsec is the distance from the Sun to this celestial object if the angle between the perpendicular and the line connecting the Earth to the celestial object is one arcsecond (1/3600 of a degree). This gives us the following right-angled triangle (the distance from the Earth to the Sun is 1 AU):



$$\tan{1''} = \tan{\left (\frac{1}{3600}^\circ\right )} = 4.85 \times 10^{-6} = \frac{1}{\mbox{parsec}}$$

Therefore, a parsec is 206,265 AU.

Questions
1. What is one parsec in m?

2. Convert 3 light days into km.

3. Convert 5.5 parsecs into light years.

4. The difference in angle of a star on the perpendicular to the plane of the Earth's orbit which passes through the Sun when viewed from either side of the Earth's orbit is 0.1°. How far away is the star in parsecs?

/Worked Solutions/