Orbits of Artificial Satellites

Artificial satellites are not placed in the same type of orbit. The height, shape, and tilt of the orbit are decided based on the purpose of the satellite. These satellites are launched using rockets (launch vehicles) and positioned at a specific height (h) above the Earth's surface. Then, they are given a specific tangential velocity, called critical velocity (Vc), which allows them to remain in orbit due to the balance between gravitational pull and their circular motion.

Critical Velocity Formula:

The satellite experiences a centripetal force which keeps it in orbit. This force is provided by the Earth's gravitational attraction.

Orbit of an artificial satellite

Centripetal Force = Gravitational Force

\[\frac{\mathrm{mv_{c}}^{2}}{\mathrm{R+h}}=\frac{\mathrm{GMm}}{(\mathrm{R+h})^{2}}\]

\[\mathrm{v_c}^2=\frac{\mathrm{GM}}{\mathrm{R+h}}\]

\[\mathbf{v}_{\mathrm{c}}=\sqrt{\frac{\mathrm{GM}}{\mathrm{R}+\mathrm{h}}}\]

Where:

• G = 6.67 × 10⁻¹¹ Nm²/kg² (Gravitational constant)
• M = 6 × 10²⁴ kg (Mass of Earth)
• R = 6.4 × 10⁶ m (Earth’s radius)
• h = Height of satellite above Earth

This formula shows that critical velocity does not depend on the mass of the satellite. As height increases, the required critical velocity decreases.

Orbits of satellites

• Satellites are placed into orbit using launchers and require a specific tangential speed (the critical velocity).
• Low Earth Orbits (180–2000 km) are used for space stations and weather studies.
• Medium Earth Orbits (2000–35780 km) are used for GPS and polar satellites.
• High Earth Orbits (≥35780 km) include geostationary satellites used for TV, phone, and weather.
• The higher the orbit, the lower the speed needed; satellite speed doesn’t depend on its mass.