Measuring distances by parallax Edexcel International A Level Physics revision
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In plain words
Hold up a finger at arm's length and look at it with one eye and then the other: it seems to jump against the background. Nearby stars do the same thing over six months, as the Earth swings from one side of the Sun to the other. The smaller the jump, the further away the star.
Three things to know
- Trigonometric parallax: a nearby star is observed against the background of very distant stars from opposite sides of the Earth's orbit, six months apart. It appears to shift.
- The parallax angle p is half of the total angle the star appears to move through. The distance is d = r ÷ tan p, where r is the radius of the Earth's orbit, 1.50 × 10¹¹ m. For such tiny angles, d = r ÷ p with p in radians.
- It only works for fairly close stars. For distant ones the angle is too small to measure, and standard candles are used instead.
Worked example
A star has a parallax angle of 3.7 × 10⁻⁶ radians. Find its distance from the Earth.
- d = r ÷ p, with p in radians.
- = 1.50 × 10¹¹ ÷ 3.7 × 10⁻⁶.
- = 4.1 × 10¹⁶ m.
Tips and tricks
- The parallax angle is half the total shift seen across six months.
- A smaller angle means a more distant star.
It lands in your notebook with its questions as flashcards.
Measuring distances by parallax: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
What is seen when a nearby star is observed six months apart?
The Earth has moved to the other side of its orbit.
Why are the two observations made six months apart?
That gives the longest baseline, and so the biggest shift.
Star A has a larger parallax angle than star B. Which is closer to the Earth?
Nearer stars appear to move more.
How are the distances to very distant galaxies found?
Their parallax angles are too small to measure.
In d = r ÷ p, what must the parallax angle p be measured in?
The small-angle approximation only works in radians.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
3 questions, 7 marks. Write your answers on paper, then check them.
Measuring distances by parallax
Edexcel International A Level Physics WPH · 7 marks · papermunch.org
Name ______________________________ Date ______________
A star has a parallax angle of 1.0 × 10⁻⁶ radians. Find its distance.[2]
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1.5 × 10¹⁷ m.
Explain why parallax cannot be used to find the distance to a far-off galaxy.[2]
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The galaxy is so far away that its parallax angle is too small to measure.
Describe the measurements needed to find the distance to a nearby star by parallax.[3]
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Record the position of the star against the background of much more distant stars. Repeat six months later, when the Earth is on the opposite side of its orbit. Measure the angle the star appears to have moved through and halve it to get the parallax angle. Use this with the radius of the Earth's orbit to find the distance.
Answers: Measuring distances by parallax
- 1. 1.5 × 10¹⁷ m.
- 2. The galaxy is so far away that its parallax angle is too small to measure.
- 3. Record the position of the star against the background of much more distant stars. Repeat six months later, when the Earth is on the opposite side of its orbit. Measure the angle the star appears to have moved through and halve it to get the parallax angle. Use this with the radius of the Earth's orbit to find the distance.