Standard Candles (Cambridge (CIE) A Level Physics)

Cepheids are a type of standard candle.

Describe how standard candles can be used to determine distances to stars.

Fig. 1.1 shows the light curve of a Cepheid variable star which has a radiant flux intensity on Earth of 500 nW m⁻².

Fig. 1.1

Use Fig. 1.1 to estimate the period of the Cepheid.

Fig. 1.2 shows the relationship between luminosity and period for a group of Cepheid variables.

Fig. 1.2

Use Fig. 1.2 and your answer from (b) to calculate the distance of the Cepheid from the Earth.

Luminosity of the Sun = 3.8 × 10²⁶ W

Vega is the brightest star in the Lyra constellation with a luminosity 40 times that of the Sun and a radiant flux intensity at Earth of 21.3 nW m⁻². 

Calculate the distance of Vega from the Earth in m. 

Luminosity of the Sun = 3.85 × 10²⁶ W

Fig. 1.1 shows a chart known as the cosmic distance ladder. It details different methods of measuring astronomical distances according to the distance they can measure from Earth.

Fig. 1.1

Using Fig. 1.1, determine the best method to use to measure the distance to Vega.

1 light year = 9.46 × 10¹⁵ m

The Andromeda galaxy is known to be the closest galaxy to our galaxy, the Milky Way.

Suggest which method could be used by an astronomer to prove that Andromeda is a separate galaxy outside of the Milky Way. Explain your choice.

Recently, astronomers have observed a type 1a supernova called Encore in a distant galaxy. Measurements of the light from Encore revealed that the galaxy is 10 billion light-years away.

State the property of a type 1a supernova that makes it suitable for measuring distances.

Light from supernova Encore is collected using the James Webb Space Telescope (JWST).

The JWST detects a peak power reading of 5.3 × 10⁻¹⁶ W. Theory predicts that this reading corresponds to Encore's peak luminosity of 2.4 × 10³⁶ W.

1 ly = 9.46 × 10¹⁵ m

(i) Calculate the peak radiant flux intensity at the JWST.

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(ii) Show that the collecting area of the JWST is 25 m².

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After the initial explosion, the light emitted by supernova Encore was collected for around 100 days. The total energy released during this time is estimated to be 10⁴⁴ J. 

Calculate the average power output of supernova Encore.

Solar panels consisting of combinations of photovoltaic cells use energy in the radiation received from the Sun to generate electricity.

An advertisement for solar panels claims that the intensity of radiation from the Sun incident at the top of the Earth’s atmosphere is more than 2 kW m⁻².

Assess the validity of this claim.

Use the following data:

• radius of Sun = 6.96 × 10⁸ m

• surface temperature of Sun = 5790 K

• distance from Sun to Earth = 1.50 × 10¹¹ m

A space probe is sent on a mission from Earth to Mars.

Power for the space probe is provided by solar panels that collect radiant energy from the Sun. The solar panels have a total area of 31 m² and are directly facing the Sun throughout the journey. The efficiency of the solar panels is 30%.

The mean orbital radius of Mars about the Sun is 2.3 × 10¹¹ m.

Compare the power available to the probe when it leaves Earth's atmosphere to the power available on its arrival at Mars.

Neptune is the farthest known planet from the Sun in the Solar System. Its distance from the Sun is 30 times greater than the distance of the Earth from the Sun.

A similar space probe to the one in (b) is sent on a mission to Neptune.

(i) Calculate the area of solar panels that would be required to achieve the same availability of power at Neptune as the space probe in (b) when it was at Mars.

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(ii) The International Space Station (ISS) currently holds the record for the largest array of solar panels in space, spanning a total area of 3244 m² to supply all of its power. 

Using this information, and your answer to (c)(i), comment on the current viability of the mission to Neptune.

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