Stellar aberration and the speed of light
The umbrella problem again, but the rain is starlight and the walker is the Earth. A tilted telescope gives the speed of light.
Point a telescope straight at a star overhead and you miss it. The telescope is fine. The Earth is moving. It is exactly why you tilt an umbrella forward when you walk in the rain.
Stellar aberration is caused by…
The Earth’s orbital speed is 2.98 × 10⁴ m s⁻¹ and the speed of light is 3.00 × 10⁸ m s⁻¹. The value of tanα is…
A telescope is tilted forward to see a star. Six months later, to see the same star it must be tilted…
A star overhead shifts by 20.5″ when the Earth’s speed is 29.8 km s⁻¹ at right angles to the light. The speed of light is…
In the rain-and-umbrella comparison, the rain plays the role of…
Compared with parallax, the size of stellar aberration depends on the distance to the star…
Explain the link between tilting an umbrella in the rain and tilting a telescope to see a star. Include the equation and say what each symbol is in each case.
Rain falls at 8 m s⁻¹ and you walk at 2 m s⁻¹. The umbrella should lean by…
The velocity of A relative to B is…
Key points
- • A moving observer sees what falls toward them slanted: relative velocity = its velocity minus the observer’s.
- • Telescope tilt (stellar aberration): tanα = v / c, about 9.93 × 10⁻⁵ rad, which is 20.5 arcseconds.
- • The tilt reverses six months later; over a year a star traces a tiny ellipse (a circle at the orbit’s pole, a line in its plane).
- • Measuring α and knowing v gives c = v / tanα, about 3.00 × 10⁸ m s⁻¹.
Formulas
- tanα = v / c
- v = 2πr / T
- c = v / tanα
Key terms
- Stellar aberration :
- the apparent shift of a star’s position caused by the Earth’s velocity
- Arcsecond :
- 1/3600 of a degree
Common errors
- • Forgetting to convert the angle from arcseconds to radians.
- • Thinking aberration depends on the star’s distance.
- • Using v in km s⁻¹ and c in m s⁻¹.