GCSE Astronomy Worksheet

GCSE Astronomy: Heliocentric Parallax and Variable Stars

Aims: Practicing key maths skills and exam-style questions.

Question 1

a) What is an arcsecond?

1/3600 of a degree

b) How many arcseconds are there in 0.1 degrees?

360

c) How many arcseconds are there in 6.5 × 10⁻⁶ degrees?

0.0234

Question 2

a) Draw a diagram below showing how heliocentric parallax can be used to find the distance to nearby stars.

[Placeholder for Parallax Diagram]

b) State the formula relating distance to a star in parsecs (d) and parallax angle in arcseconds (p).

d = 1 / p

c) A nearby star has a parallax angle of 4.2 × 10⁻⁵ degrees. Calculate the distance to this star.

Calculation:
1. Convert degrees to arcseconds: 4.2 × 10⁻⁵ × 3600 = 0.1512
2. Apply formula: d = 1 / 0.1512
3. Answer: 6.6 pc

Question 3

a) What is an RR Lyrae variable star?

  • Periodic, pulsating variable stars
  • Commonly found in globular clusters

b) What is an eclipsing variable star?

  • Pair of stars orbiting each other/their common centre of mass.
  • The plane of the orbit passes through/near Earth.
  • One star passes in front of the other.
  • The total magnitude observed decreases (the amount of light Earth receives decreases).

c) What is a Cepheid variable star?

  • Variable star that pulses radially.
  • Varying in both diameter and temperature.
  • Periodic change in brightness.
  • Stable amplitude changes.

d) Explain how astronomers can use Cepheid Variables to calculate distances.

  • Period is related directly to its luminosity (Period-Luminosity Law).
  • Allows astronomers to work out absolute magnitude (M).
  • Apparent magnitude (m) is measured.
  • Using M = m + 5 - 5log d, they can calculate the distance (d).

Question 4: Light Curves

Draw the light curve for each type of variable star and label them.

Marking guide: 1 mark for correct axes, 1 mark for each correct diagram (RR Lyrae, Eclipsing, Cepheid).

Question 5: Eclipsing Variable Analysis

Shown below is the light curve of an eclipsing variable.

[Placeholder for Light Curve Image]

a) Explain what each of the dips in magnitude represent.

  • First dip: Dimmer star passing in front of brighter star for the first time.
  • Second dip: Dimmer star going behind the brighter star from our point of view.
  • Third dip: Dimmer star passing in front of the brighter star for the second time.

b) State the period of this eclipsing variable system.

10 units of time.