- How a spacecraft will remain in orbit forever.
|Hi. I'm not expert in physics. Recently I have written an article how a spacecraft will remain in orbit forever. However need review if there is any mistake using formulas or the term escape velocity. Here is it,|
Quick Answer: Yes it will reach the orbit. But what do you think about its orbital motion? It will fall back to earth.
Explanation: Consider two spacecrafts. Suppose a plasma technology based sci-fi spacecraft travelling at constant velocity of 20 Km/hr hence zero acceleration while conventional spacecraft is using burning fuel travelling with nominal acceleration of 9.8 m/s/s.
Sci-fi spacecraft: Consider a scenario, suppose we are travelling in a car. At constant velocity of 20 Km/hr we can reach a horizontal distance of 200 Km in 10 hrs.
S = 200 Km
V = 20 Km/hr
S = Vt
S = 200 * 1000 = 200000 m
V = (20 * 1000) m/(60*60) s
t = S/V
t = (200000 * (60 * 60)) /20000
t = 36000 s = 10 hrs
Now consider the case of vertical takeoff of ours sci-fi spacecraft. It will still take 10 hrs to reach orbit.
Conventional spacecraft: We know that any free falling body travels to earth at constant acceleration of 9.8 m/s/s. So the reverse is also true. If a spacecraft has to escape from earth completely it has to at least accelerate against it at 9.8m/s/s. The velocity it will attain at certain orbital distance is called escape velocity. The formula gets changed in such case as below,
S = Vi*t + 0.5*g*t^2
Suppose initial speed is zero.
Vi = 0 m/s
S = 200 Km = 200 * 1000 = 200000 m
200000 = 0 + .5 * 9.8 * t^2
t = 202 s
Thus it will take only 202 s to cover 200 Km vertically.
Vf = Vi + gt
Vf = 0 + 9.8 * 202
Vf = 1980 m/s = (1980 * (60 * 60))/1000 = 7126 Km/hr
Thus it will reach escape velocity of 7126 Km/hr when in orbit.
The deciding factor: We noted that we reached orbit whether it is conventional spacecraft with escape velocity of 7126 Km/hr and acceleration of 9.8 m/s/s while following a tangential curved path or sci-fi spacecraft with constant velocity of 20 Km/hr and zero acceleration while following a vertical path. At 200 Km they both stopped engines. There is no air friction so now conventional spacecraft is also moving with zero acceleration or deceleration i.e. there is no increase or decrease in its velocity. The earth’s gravitational field will continue bending the path of conventional spacecraft in a circle and it will remain in its orbit forever. While sci-fi spacecraft after stopping its engine falls back to earth while accelerating downward after a while. Hence It is the escape velocity at certain orbit that is the deciding factor of its fortune.