A mini satellite weighing 50 kg is going to be launched into an orbit around earth by a rocket. One sidereal day (period of earth’s self-orbit) is 23 hours, 56 minutes and 4.1 seconds. (a) The rocket is to be launched from a platform in the Mongolian Plateau with a height of 3.5 km above earth surface. Calculate the acceleration due to earth’s gravity at this elevation. (b) The satellite shall complete 10 orbits in precisely 1 sidereal day. Calculate the orbital height and orbital velocity of the satellite. (c) Once the satellite is in this orbit, what is the acceleration due to earth’s gravity experienced by the satellite? (d) Referring to your answer in part (c), explain why the satellite does not fall towards earth as a result of earth’s gravitational pull?
Gravitational force
In nature, every object is attracted by every other object. This phenomenon is called gravity. The force associated with gravity is called gravitational force. The gravitational force is the weakest force that exists in nature. The gravitational force is always attractive.
Acceleration Due to Gravity
In fundamental physics, gravity or gravitational force is the universal attractive force acting between all the matters that exist or exhibit. It is the weakest known force. Therefore no internal changes in an object occurs due to this force. On the other hand, it has control over the trajectories of bodies in the solar system and in the universe due to its vast scope and universal action. The free fall of objects on Earth and the motions of celestial bodies, according to Newton, are both determined by the same force. It was Newton who put forward that the moon is held by a strong attractive force exerted by the Earth which makes it revolve in a straight line. He was sure that this force is similar to the downward force which Earth exerts on all the objects on it.
A mini satellite weighing 50 kg is going to be launched into an orbit around earth by a
rocket. One sidereal day (period of earth’s self-orbit) is 23 hours, 56 minutes and 4.1
seconds.
(a) The rocket is to be launched from a platform in the Mongolian Plateau with a height
of 3.5 km above earth surface. Calculate the acceleration due to earth’s gravity at
this elevation.
(b) The satellite shall complete 10 orbits in precisely 1 sidereal day. Calculate the
orbital height and orbital velocity of the satellite.
(c) Once the satellite is in this orbit, what is the acceleration due to earth’s gravity
experienced by the satellite?
(d) Referring to your answer in part (c), explain why the satellite does not fall towards
earth as a result of earth’s gravitational pull?
(e) Calculate the total energy of the satellite in orbit, using infinity as frame of
reference.
(f) Calculate the escape velocity to leave earth’s gravitational well.
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