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All objects possess gravitational potential energy which is defined as the potential amount of work done by gravity for a certain displacement s. `U=mgh`
Note: the reason why we define the equation using an infinity point because it is consistent regardless of an object’s position in the gravitational field. At distance `oo`, Ep approaches 0, as we move the object from this point, the value of r decreases, and theoretically its potential energy should also decrease. Therefore, as a result of how we define the equation, the potential energy becomes more negative.
`W = -(GMm)/(r_f)+(GMm)/(r_i)` Practice Question 4 Define the term Gravitational Potential Energy. Practice Question 5 A satellite with a mass of 200 kg maintains its orbit at an altitude of 300 km above the Earth’s surface. The Earth has a radius of 6.371 x 106 m and a mass of 6.00 x 1024 kg. (a) Determine the gravitational potential energy of the satellite at this altitude. (2 marks. (b) Calculate the work done to move this satellite to an altitude of 4000 km above Earth’s surface. (2 marks) Kinetic Energy Besides possessing gravitational potential energy, all objects in motion in space possess kinetic energy given by the equation: By substitution velocity as orbital velocity:
Total Energy
`T= (GMm)/(2r) – (GMm)/r`
This is consistent with an increase in orbital velocity
Escape Velocity
Imagine an object travelling faraway enough to finally escape the effect of gravity. By Newton’s universal law of gravitation, this scenario can only occur at r = `oo`
`K+U=0` `1/2mv^2=(GMm)/r` `v^2=(2GM)/r` `v_(esc)=sqrt((2GM)/r)` We can determine the minimal velocity required to allow an object to escape the gravitational field it is in.
Practice Question 6 A satellite of mass 1000 kg has been launched from the surface of Earth and sometime later then potential energy of the satellite was determined to be – 3.97 J. Determine the distance of the satellite from Earth at this point and hence the escape velocity of the satellite (4 marks) Practice Question 7 Compare the escape velocity of low-Earth and geostationary satellites of equal mass (2 marks) Previous section: Kepler's Laws of Planetary Motion Next section: Low Earth and Geostationary Orbit Satellites
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