Please find attached the diagram of the different thrust of the spaceship created with Microsoft Visio with the numbers representing the following situations

(1) Thrust is less than weight. The spaceship does not launch

(2) Thrust is just a little greater than weight. The net force gives the spacecraft acceleration up, but not enough to gain the speed needed to reach orbit

(3) Thrust is greater than weight. The net force gives the spacecraft acceleration up. It gains enough speed to "fall around" Earth, constantly moving in a nearly circular path

(4) Thrust is a lot greater than weight. The very large net force gives the spacecraft a very large acceleration up. It gains so much speed that it escapes Earth

Explanation:

1) The thrust F < Weight = Mass of spacecraft, m × The acceleration due to gravity, g

F < W = m × g, the spacecraft remains on the Earth surface

2) The thrust, F > W, The space craft has an initial upwards acceleration, given by (F - W)/m

$v < v_{orbit} \ Orbital \ velocity =\sqrt{\dfrac{G \cdot M}{r} }$

3) F > W and $v =v_{orbit} = \sqrt{\dfrac{G \cdot M}{r} }$

4) F > W and $v \geq v_{esc} = \sqrt{\dfrac{2 \cdot G \cdot M}{r} }$

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3 years ago