The Solar System

Structure of the Solar System

The Solar System consists of the Sun at its centre, which is a star that provides light and heat. Around the Sun orbit eight major planets in nearly circular paths:

• Mercury
• Venus
• Earth
• Mars
• Jupiter
• Saturn
• Uranus
• Neptune

Besides these, there are dwarf planets such as Pluto, which are smaller and have not cleared their orbits of other debris.

Other objects include:

• Asteroids: Rocky bodies mostly found in the asteroid belt between Mars and Jupiter.
• Comets: Icy bodies that develop tails when near the Sun due to sublimation of ice.

All these bodies orbit the Sun due to its gravitational pull.

Orbital Motions

The motion of planets and other bodies around the Sun is governed by gravity. The Sun’s gravity provides the centripetal force needed to keep planets moving in their orbits.

Orbits can be:

• Circular: The distance between the planet and the Sun remains constant.
• Elliptical: Orbits are oval-shaped, so the distance varies during the orbit.

The stability of an orbit depends on a balance between the gravitational pull of the Sun and the planet’s tendency to move in a straight line (inertia). If this balance changes, the orbit may become unstable.

Non-circular orbits mean the speed of the planet changes: it moves faster when closer to the Sun and slower when further away, due to stronger or weaker gravitational force.

For example, Earth’s orbit is slightly elliptical, but close enough to circular that its distance from the Sun does not vary greatly.

Example: A planet orbits the Sun in a circular orbit of radius 1.5 × 10¹¹ m. The gravitational force provides the centripetal force to keep it moving. If the planet’s mass is $6 \times 10^{24}$ kg and its orbital speed is $3 \times 10^{4}$ m/s, calculate the gravitational force acting on it.

Using the centripetal force formula (which equals the gravitational force for orbiting planets):

$$F = \frac{mv^2}{r}$$

Substitute values:

$$F = \frac{6 \times 10^{24} \times (3 \times 10^{4})^2}{1.5 \times 10^{11}}$$

$$F = \frac{6 \times 10^{24} \times 9 \times 10^{8}}{1.5 \times 10^{11}} = \frac{5.4 \times 10^{33}}{1.5 \times 10^{11}} = 3.6 \times 10^{22} \text{ N}$$

So, the gravitational force acting on the planet is $3.6 \times 10^{22}$ newtons.

Satellites

Natural satellites are moons orbiting planets, held in orbit by the planet’s gravity. For example, Earth’s natural satellite is the Moon.

Artificial satellites are human-made objects launched into orbit for various purposes:

• Communications (e.g. TV, internet)
• Weather monitoring
• Navigation (e.g. GPS)
• Scientific research

The orbital speed of a satellite depends on its altitude above the Earth. Satellites closer to Earth must travel faster to balance the stronger gravitational pull, while those further away travel slower.

Satellites in low Earth orbit (LEO) circle the Earth quickly, completing an orbit in about 90 minutes, whereas geostationary satellites orbit much higher and take 24 hours to match Earth’s rotation, appearing fixed over one spot.

Example: Calculate the orbital speed of a satellite orbiting 300 km above the Earth’s surface. The Earth’s radius is approximately $6.4 \times 10^{6}$ m and its mass is $6.0 \times 10^{24}$ kg. Use the formula for orbital speed:

$$v = \sqrt{\frac{GM}{r}}$$

Where:

• $G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2$ (gravitational constant)
• $M = 6.0 \times 10^{24} \, \text{kg}$ (mass of Earth)
• $r = \text{Earth’s radius} + \text{altitude} = 6.4 \times 10^{6} + 3.0 \times 10^{5} = 6.7 \times 10^{6} \, \text{m}$

Calculate:

$$v = \sqrt{\frac{6.67 \times 10^{-11} \times 6.0 \times 10^{24}}{6.7 \times 10^{6}}} = \sqrt{\frac{4.002 \times 10^{14}}{6.7 \times 10^{6}}} = \sqrt{5.97 \times 10^{7}} \approx 7.73 \times 10^{3} \text{ m/s}$$

So, the satellite’s orbital speed is approximately 7,730 m/s.

Star Formation and Life Cycle

Stars form from clouds of dust and gas called nebulae. Gravity pulls the gas and dust together, forming a dense core called a protostar. As the protostar contracts, it heats up until nuclear fusion starts in its core.

The star then enters the main sequence phase, where it fuses hydrogen into helium, releasing energy that balances gravitational collapse. Our Sun is currently a main sequence star.

The life cycle depends on the star’s mass:

• Solar-mass stars (like the Sun) expand into red giants after hydrogen runs out, then shed outer layers to form planetary nebulae, leaving behind a dense core called a white dwarf. Eventually, the white dwarf cools and fades.
• Larger stars become red supergiants, then explode as supernovae. The remnant can be a neutron star or, if massive enough, a black hole.