Figure 1 shows the evolution of a star similar to the Sun on a Hertzsprung-Russell (HR) diagram. **0.1.1** State the evolutionary stage of the star at each of the points W, X, Y and Z. **0.1.2** Annotate Figure 1 with a T to show the position of Theta Carinae. **0.1.3** Explain one difficulty with using the transit method to detect this planet. **0.1.4** The astronomer suggests that the Earth-sized planet receives a similar amount of power from Theta Carinae as the Earth does from the Sun. The average power output of the Sun is 3.8 × 10^26 W. Determine the orbital radius of the Earth-sized planet orbiting Theta Carinae.

A-Level AQA Physics Classification of Stars: Figure 1 shows the evolution of

Figure 1 shows the evolution of a star similar to the Sun on a Hertzsprung-Russell (HR) diagram - AQA - A-Level Physics - Question 1 - 2021 - Paper 4

Question 1

Figure 1 shows the evolution of a star similar to the Sun on a Hertzsprung-Russell (HR) diagram. **0.1.1** State the evolutionary stage of the star at each of the p... show full transcript

Worked Solution & Example Answer:Figure 1 shows the evolution of a star similar to the Sun on a Hertzsprung-Russell (HR) diagram - AQA - A-Level Physics - Question 1 - 2021 - Paper 4

Step 1

0.1.1 State the evolutionary stage of the star at each of the points W, X, Y and Z.

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Answer

W - Protostar/gas cloud X - Main sequence star Y - Red giant and/or White dwarf Z - Supergiant

Step 2

0.1.2 Annotate Figure 1 with a T to show the position of Theta Carinae.

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Answer

Position the letter 'T' in the region that represents a star with a surface temperature of 31,000 K, roughly corresponding to the class O region on the HR diagram. Ensure that 'T' is placed within the grey box accepted region.

Step 3

0.1.3 Explain one difficulty with using the transit method to detect this planet.

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Answer

The transit method measures how much light is blocked by the planet. If the planet is small and the star is very big, then very little light is blocked out, making it challenging to detect the planet's presence.

Step 4

0.1.4 Determine the orbital radius of the Earth-sized planet orbiting Theta Carinae.

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Answer

To find the orbital radius, we can use the power relation based on the inverse square law:

$P = rac{L}{4 \pi r^2}$

Where:

$P$ is the power received by the planet (same as the power output of the Sun, $3.8 \times 10^{26} W$ ),
$L$ is the luminosity of Theta Carinae (assumed to be similar to that of the Sun),
$r$ is the orbital radius.

Rearranging the formula to find $r$ results in:

$r = \sqrt{\frac{L}{4 \pi P}}$

By substituting the necessary values (assuming Theta Carinae has similar luminosity to the Sun), we find:

$r \approx 1 \text{ AU}$ .

Figure 1 shows the evolution of a star similar to the Sun on a Hertzsprung-Russell (HR) diagram - AQA - A-Level Physics - Question 1 - 2021 - Paper 4

Worked Solution & Example Answer:Figure 1 shows the evolution of a star similar to the Sun on a Hertzsprung-Russell (HR) diagram - AQA - A-Level Physics - Question 1 - 2021 - Paper 4

0.1.1 State the evolutionary stage of the star at each of the points W, X, Y and Z.

0.1.2 Annotate Figure 1 with a T to show the position of Theta Carinae.

0.1.3 Explain one difficulty with using the transit method to detect this planet.

0.1.4 Determine the orbital radius of the Earth-sized planet orbiting Theta Carinae.

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