Q2 Many communication satellites (satcoms) are fixed in geostationary orbits.What type of force is required to keep the satcoms in orbit? What is the direction of this force?
They orbit around the equator at a height of 35 800 km. Calculate the acceleration due to gravity at this distance above the surface of the Earth. (Gravitational constant, G 6.7 1011 N m2 kg2; radius of the Earth, R 6.4 106 m; mass of the Earth,M 6.0 1024 kg)
What is the linear velocity of these satellites? T2
4p2(R h)3 GM
, where T is the period of the satellite, R is the radius (6)
(12) (9)
Show that for any satellite of mass m which orbits the Earth in a circular orbit at a constant height h above the surface of the Earth,
of the Earth, G is the gravitational constant and M is the mass of the Earth.
Many satellites are positioned above and below the 358 km required for a stationary satellite.What happens to the period of orbit when the satellite is further away from the surface of the Earth?
The international space station (ISS) orbits the Earth around the equator at a height of 400 km. Calculate the period of an orbit of the ISS.
(15) (5) (9)
‘SECTION B’
HALF QUESTION Typical of Question 12 in Leaving Cert. Exam
Q3 Answer both of the following parts (a) and (b). (a) State Newton’s law of universal gravitation.
The distance between the Earth and the Sun is 1.5 1011 m. It takes the Earth 365.25 days to orbit the Sun.
(i) Calculate the speed of the Earth as it orbits the Sun. (ii) Calculate the mass of the Sun. (G 6.7 1011 N m2 kg2)
(b) Derive the relationship between the velocity of a particle travelling in uniform circular motion and its angular velocity.
Describe an experiment to demonstrate that the force required to keep a body in uniform circular motion increases as the speed of the body increases, while maintaining a constant radius.
Calculate the force required to keep a body of mass 50 g travelling in a circle of radius 40 cm at a speed of 3 m s1.
