# Spacecraft orbital motion

## Summary:

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,
Layman question: So what will happen if we use sci-fi spacecraft to takeoff from earth, move at constant velocity and then follow orbital motion around earth? It is using plasma technology instead of conventional burning fuel. The constraint is spacecraft technology is at initial stage and can’t move fast like conventional rockets. There is not a big issue how much time it will take.

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.

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A.T.
However need review if there is any mistake using formulas or the term escape velocity.
Why is escape velocity relevant at all for orbital motion?

Layman question: So what will happen if we use sci-fi spacecraft to takeoff from earth, move at constant velocity and then follow orbital motion around earth?

Explanation:
.... At 200 Km they both stopped engines.
I don't see the stopping engines part in the question.

Ibix
I'm a bit unclear what you are asking here. I think you are trying to discuss an engine capable of driving a spaceship to climb vertically at constant speed. This is certainly possible, although fuel considerations are likely to be an issue. You simply need an engine capable of producing a thrust equal to the weight of the craft - that is, an acceleration of 1g. That effectively cancels the pull of gravity, and you can start it moving upwards with a swift kick (neglecting air resistance).

The problem, as you seem to be aware, is that you have no orbital velocity, so when you turn off the engine you start to fall straight down. This is easy enough to overcome - simply up the thrust slightly and tip the rocket over a bit.

As I understand it, the fundamental problem with your low thrust approach is that you have to carry ridiculous quantities of fuel because you soend such aong time under thrust.

Lnewqban
Quick Answer: Yes it will reach the orbit. But what do you think about its orbital motion? It will fall back to earth.
If it reaches the orbit it doesn't fall back to Earth. If it falls back to Earth it didn't reach the orbit. It seems you don't consider that reaching the orbit requires orbital velocity.

Janus
Staff Emeritus
Gold Member
Summary:: 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,
Layman question: So what will happen if we use sci-fi spacecraft to takeoff from earth, move at constant velocity and then follow orbital motion around earth? It is using plasma technology instead of conventional burning fuel. The constraint is spacecraft technology is at initial stage and can’t move fast like conventional rockets. There is not a big issue how much time it will take.

Quick Answer: Yes it will reach the orbit. But what do you think about its orbital motion? It will fall back to earth.
To "reach" orbit you have to be moving at orbital speed for the altitude. At most, you can say that the craft has reached a particular orbit's altitude.
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.
7126 km/hr (1.98 km/sec) is nowhere near the 7.78 km/sec needed to maintain a circular orbit at an altitude of 200 km. Escape velocity at that altitude is 11 km/sec.
Escape velocity is the speed you have to be moving at a given distance from the center of a planet or other body so that you not only don't fall back if you cut your engines, but you would keep flying away from the planet in question ( and not held in an closed orbit around it)
It is ##\sqrt{2}## times the velocity needed to maintain a circular orbit around the planet at that distance.

Lnewqban