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617-Champs : Gravitation homework (English)
. In this question the earth (Mass MT) should be considered as a homogeneous non-rotating sphere with radius RT. All friction should be neglected. Given : RT = 6,38.106 m MT = 5,98.1024 kg gravitational constant G = 6,67.10-11 N.m2.kg-2
Show that from the given values for the constants, it can be deduced that the acceleration of the gravitational force at the surface of the earth go equals 9,80m.s-2.
21 From the surface of the earth a rocket with mass m is launched in a direction perpendicular to that surface. Show that the work W that must be done to reach the maximum height h is given by the formulae W = G.MT.m.(RT-1 - (RT + h)-1)
22 Show that the expression given for the work W also can be written as W = m.go.h.RT(RT + h)-1
23 Calculate the work W1 to be done to let a rocket with a mass m = 3,00.104 kg reach a maximum height h1 = 1,50.103 km
24 Calculate the minimal work W to be done to bring the rocket at infinite distance from the earth.
31 The rocket now is moving in a circular orbit at a height h1 = 1,50.103 km. Calculate the revolution time T1 of the rocket in its orbit.
32 One wants to bring the rocket to an orbit where the revolution time is larger. Is the velocity in new orbit greater, smaller or equal to the original one ? Explain why.