Satellites, which play an increasing role in the information age, are controlled by the gravitational force - Leaving Cert Physics - Question 6 - 2019

The relationship between the period (T) of a satellite and the radius (r) of its orbit is given by Kepler's third law, which states that:

$T^2 \propto r^3$

This means that the square of the orbital period is proportional to the cube of the semi-major axis of its orbit.

Infrared radiation has a longer wavelength than visible light. In the electromagnetic spectrum, infrared radiation falls just beyond the visible spectrum, ranging from approximately 700 nm to 1 mm.

Infrared radiation can be detected using a thermocouple or a thermopile, which measure temperature changes. Alternatively, infrared sensors or photodiodes sensitive to infrared wavelengths can be utilized to measure the intensity of infrared radiation.

The period of METEOSAT 11 is 24 hours, allowing it to maintain a geostationary position above the equator.

The height (h) of the satellite above the Earth's surface can be calculated using the formula derived from Kepler's law:

$T^2 = \frac{4 \pi^2}{G m_{Earth}} (R + h)^3$

Given that the period T = 86400 s and using the mass of Earth, the calculations yield:

$R = 6400 \text{ km} \implies h \approx 3578 \text{ km}$

To find the radius of orbit (R), we use the relationship of orbital speed (v):

$v^2 = G \frac{m_{Earth}}{R}$

Given v = 14000 km/h = 3889 m/s,

Solving gives:

$R \approx 2650 \text{ km}$

The angular velocity (ω) can be calculated from the speed:v = ωR. Rearranging gives:

The time (t) for a signal to travel to Earth is calculated using:

$t = \frac{d}{c}$

where d is the distance (R) and c is the speed of light (3.0 × 10^8 m/s). Using R = 2650 × 10^3, we find:

t ≈ 0.0089 s (approximately, resolving for the total distance).

Satellites remain in orbit due to their high tangential velocity and the balance between gravitational force and the inertial force acting on them. As they travel forward, gravity pulls them towards the Earth, creating a stable orbit where they continuously fall toward the Earth but also move forward, preventing them from crashing into it.