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Physics - Stars and the Universe

Grade 9IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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The Solar System consists of the Sun, eight planets (Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune), dwarf planets, asteroids, and comets.

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The Sun is a medium-sized star that contains mostly hydrogen and helium. It radiates energy due to nuclear fusion of hydrogen into helium in its core: 411H→24He+2+10e+energy4 _{1}^{1}H \rightarrow _{2}^{4}He + 2 _{+1}^{0}e + \text{energy}

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Orbital motion is maintained by gravitational force. For a circular orbit, the orbital speed vv is constant, but the velocity is constantly changing because the direction of motion is changing.

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A Light Year is the distance light travels in a vacuum in one year, approximately equal to 9.5×1015 m9.5 \times 10^{15} \text{ m}.

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Stars are formed from interstellar clouds of gas and dust (nebulae) collapsing under gravity to form a protostar. The lifecycle of a star depends on its initial mass.

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Life cycle of a star like the Sun: Nebula→Protostar→Main Sequence→Red Giant→Planetary Nebula→White Dwarf\text{Nebula} \rightarrow \text{Protostar} \rightarrow \text{Main Sequence} \rightarrow \text{Red Giant} \rightarrow \text{Planetary Nebula} \rightarrow \text{White Dwarf}

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Life cycle of a massive star: Nebula→Protostar→Massive Star→Red Supergiant→Supernova→Neutron Star or Black Hole\text{Nebula} \rightarrow \text{Protostar} \rightarrow \text{Massive Star} \rightarrow \text{Red Supergiant} \rightarrow \text{Supernova} \rightarrow \text{Neutron Star or Black Hole}

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Redshift is the observed increase in the wavelength of light from distant galaxies, indicating they are moving away from us. This provides evidence for the Big Bang theory and the expansion of the universe.

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Hubble's Law states that the recession velocity vv of a galaxy is proportional to its distance dd from Earth: v=H0dv = H_{0}d where H0H_{0} is the Hubble constant, approximately 2.2×10−18 s−12.2 \times 10^{-18} \text{ s}^{-1}.

📐Formulae

v=2πrTv = \frac{2 \pi r}{T}

v=H0dv = H_{0}d

d=vH0d = \frac{v}{H_{0}}

t≈1H0t \approx \frac{1}{H_{0}}

💡Examples

Problem 1:

The Earth orbits the Sun at an average distance of 1.5×108 km1.5 \times 10^{8} \text{ km}. Given that it takes 365.25365.25 days to complete one orbit, calculate the orbital speed in km/s\text{km/s}.

Solution:

First, find the time TT in seconds: T=365.25×24×60×60≈3.156×107 sT = 365.25 \times 24 \times 60 \times 60 \approx 3.156 \times 10^{7} \text{ s} Now use the orbital speed formula: v=2πrTv = \frac{2 \pi r}{T} v=2×3.142×1.5×108 km3.156×107 sv = \frac{2 \times 3.142 \times 1.5 \times 10^{8} \text{ km}}{3.156 \times 10^{7} \text{ s}} v≈29.9 km/sv \approx 29.9 \text{ km/s}

Explanation:

To find the orbital speed, we divide the circumference of the circular path (2πr2 \pi r) by the orbital period (TT).

Problem 2:

A distant galaxy is observed to have a recession velocity of 3.0×106 m/s3.0 \times 10^{6} \text{ m/s}. Using a Hubble constant of 2.2×10−18 s−12.2 \times 10^{-18} \text{ s}^{-1}, calculate the distance to this galaxy in meters.

Solution:

Using Hubble's Law formula: v=H0dv = H_{0}d Rearrange for dd: d=vH0d = \frac{v}{H_{0}} d=3.0×106 m/s2.2×10−18 s−1d = \frac{3.0 \times 10^{6} \text{ m/s}}{2.2 \times 10^{-18} \text{ s}^{-1}} d≈1.36×1024 md \approx 1.36 \times 10^{24} \text{ m}

Explanation:

By dividing the recession speed by the Hubble constant, we can estimate the distance of a galaxy from Earth.

Problem 3:

Estimate the age of the universe in years using the Hubble constant H0=2.2×10−18 s−1H_{0} = 2.2 \times 10^{-18} \text{ s}^{-1}.

Solution:

The age of the universe tt is approximately the reciprocal of the Hubble constant: t=1H0t = \frac{1}{H_{0}} t=12.2×10−18 s−1≈4.545×1017 st = \frac{1}{2.2 \times 10^{-18} \text{ s}^{-1}} \approx 4.545 \times 10^{17} \text{ s} To convert to years: t=4.545×1017365.25×24×3600t = \frac{4.545 \times 10^{17}}{365.25 \times 24 \times 3600} t≈1.44×1010 years (approx 14.4 billion years)t \approx 1.44 \times 10^{10} \text{ years (approx 14.4 billion years)}

Explanation:

The ratio of distance to velocity (d/vd/v) gives an estimate of how long the universe has been expanding, which is equal to 1/H01/H_0.