A satellite is an object in space that orbits around a larger body, such as a planet. There are two different types of satellites:
Natural satellites are objects in space that orbit around a planet. They are also known as moons and are not artificial and serve various purposes, such as the moon helping stabilise Earth’s rotation and affecting the tides.
Moon and the other stars revolve around the earth.
Artificial satellites are man-made objects that are sent into space to orbit around the Earth or other celestial bodies. These satellites are used for a variety of purposes, including communication, navigation, scientific research, and military surveillance.
Satellites are launched into space through the use of powerful rockets. The rockets are designed to propel the satellites high up into the atmosphere and break free from the Earth’s gravity. To achieve this, they burn a significant amount of fuel, enabling them to reach orbit around the Earth. Once the rocket reaches a specific altitude and speed, the satellite separates from the rocket and begins to orbit the Earth. The satellite is equipped with engines and guidance systems, which enable it to adjust its orbit and maintain its position to perform its intended function.
Communication:
Artificial satellites are used for communication, transmitting phone calls, TV signals, and internet data.
Global Positioning System (GPS):
Artificial satellites are also used for navigation, such as GPS (Global Positioning System) satellites. They orbit at high altitudes, and GPS receivers on the ground use signals from multiple satellites to calculate precise locations.
Exploration:
Artificial satellites are also used for scientific research. Space telescopes like the Hubble Space Telescope are used for observing stars, galaxies, and other celestial objects.
Orbits:
The path that the satellite follows around the Earth is called its orbit. The time to complete its orbit varies as per the altitude and the angle of its rotation.
The law of gravity made by Newton explains how satellites can move in their orbits. This law can also be used to calculate the centripetal force required for a satellite to revolve around the Earth.
To calculate the velocity of a satellite, we will need to assume a few values.
Consider:
m → Mass of the Satellite
M → Mass of the Earth
R → Radius of the Earth
h → Height (Altitude) Of the Satellite From the Surface of Earth
r = R + h → Radius of Orbit
We know that,
Centripetal Force = Gravitational Force
Where FC is Centripetal Force
Mathematically,
\({F_C}={F_G}\) →(i)
∵ \({F_C}=\frac{mv^2}{r}\)
and
\({F_G}=\frac{GmM}{r^2}\)
Substituting the values of FC and FG in equation (i):
\(\frac{mv^2}{r} =\frac{GmM}{r^2}\)
\(v^2=\frac{GM}{r} [ ∵ r = R + h ]\)
\(∵ v = \sqrt{\frac{GM}{R+h}}\)
OR
v = √GM/R + h
This formula gives the velocity of a satellite in orbit of the Earth. Remember, no matter how big or small a satellite is, it will move at the same speed when it orbits around something.
To calculate the time required for a satellite to complete a revolution around its orbit, we will need to do the following steps:
T → Time Required by a Satellite to Complete a Revolution Around Its Orbit
Mathematically,
∵\(T = \frac{2\pi r}{v}\) →(i)
To calculate the time needed for the satellite to complete its orbit, we need the equation from before
\(v = \sqrt{\frac{GM}{R+h}}\)
By substituting the formula of velocity of satellite in equation (i), we get
∴\(T = \frac{2\pi r}{\sqrt{GMR}}\)
∵\( r = R + h\)
∵\( T=2\pi r \sqrt\frac{r}{GM}\)
∴\(T = 2\pi \sqrt{\frac{r^3}{GM}}\)
OR
T = 2π√(r3/GM)