Question about falling bodies in orbit and acceleration

[LBrandt]

Hello,

I’m glad that I found this forum, because there is a question that has been bothering me for some time, and maybe someone on a physics forum like this can set me straight on it. It concerns gravity and acceleration.

I understand that when an object such as a space shuttle is placed into orbit around a massive body such as the Earth, the object is actually “falling” and is able to continue its orbit because its attempt to escape orbit is matched by gravity, and it continues in a circular “fall”. I also understand that an astronaut can exit such a vehicle in orbit and that the astronaut will continue to orbit with the vehicle, without the vehicle leaving him behind.

My problem comes when I see a depiction of an astronaut exiting a spaceship that is NOT in orbit. For instance, in many movies (2001 A Space Odyssey, for example) the astronaut leaves the spaceship, and as with the astronaut exiting a vehicle in orbit, is NOT left behind by the spaceship. This same scenario has been portrayed in many sci-fi movies, not just 2001.

How can this be? If the spaceship is NOT in orbit (therefore NOT “falling”), but in fact is in interplanetary space and on a mission to Mars e.g., doesn’t the spaceship have its engines operating, and therefore how can the astronaut remain with the spaceship, when the spaceship is under rocket power and the astronaut isn’t?

Thank you,
Louis

 

[Filip Larsen]

Welcome to PF!

When the astronaut exits his spaceship and both are affected only by gravity forces (that is, neither the spaceship nor the astronaut is firing any rocket engines), the resulting magnitude and direction of acceleration is, due to Newtons law of gravity and his law of motion, almost equal to each other making the two "bodies" move or "fall" in the same manner thus following the same trajectory. Its kind of like if you have two race cars with identical acceleration profiles that start from stand still next to each other - they too could accelerate to high speed but still stay very close to each other because they both "do" the same acceleration (granted, race cars drivers usually race to win, so they are likely to pull ahead of the competition if they can).

Note, that the "same acceleration" above is a result of the two bodies being in (almost) same position relative to the massive objects, like Earth, and it does not depend on which orbit the two bodies follow initially. However, as distance between the two object increases (like if the astronaut after a little push let himself drift away from his spaceship) the acceleration will in most cases begin to differ just enough for the two so that their trajectory will begin to diverge. Depending on the conditions, such initially diverging trajectories may continue to diverge for all times or, like when they are in orbit around a planet or sun, may result in the two bodies getting close to each other again at some later point in time. The precise way this works is the subject of orbital mechanics and while simple in principle, it can give rise to some complicated and counter-intuitive situations (this I say so you don't come away thinking that there is one answer that covers all situations).

 

[LBrandt]

Thanks for your reply, but I still don't quite understand. If, in the example of the astronaut exiting an orbiting space shuttle in Earth orbit, the shuttle engines were to immediately fire, then surely the astronaut would no longer be able to remain with the shuttle. If this is the case, then why is the astronaut who exits a spaceship in interplanetary or intestellar flight, with its engines firing, able to stay with the ship?
Louis

 

[George Jones]

If this is the case, then why is the astronaut who exits a spaceship in interplanetary or intestellar flight, with its engines firing, able to stay with the ship?
Louis

In this scenario, the astronaut is not able to stay with the ship. Note, however, that a spaceship in interplanetary or interstellar flight does not have to have its engine firing.

 

[LBrandt]

Thanks, but I believe that a spaceship in interplanetary or instellar flight would, in fact, have its propulsion system operating constantly. In fact, there have been some suggestions that one way to speed up long distance space flight would be to use a solar sail, accelerating the ship to higher and higher velocities. I doubt that an interstellar or even an interplanetary spaceship would make any progress without constant propulsion, at least until it began to achieve orbital insertion at its destination planet.
Louis

 

[Filip Larsen]

You are correct that it is a kind of a design goal for the space industry to make propulsion systems that are more energy efficient, which as a result normally would mean it also has to operate over longer periods of time. However, so far such technology has only been employed on a few probes (like Deep Space 1) since the resulting acceleration is very low (in the order of milli-gees). In contrast, the "traditional" chemical engine is capable of high accelerations but only for short periods time, meaning it will coast most of the time.

You are also correct that most space movies get space flight all wrong. I gather we can thank old George Lucas for introducing, or at least popularize, many of the misconception in movies today. I would not be surprised if some survey would reveal that the majority of otherwise well-educated people now think that the way spaceships move in Star Wars is quite realistic.

However, Space Odysee 2001 is not among those films and depicts most of the mechanics correctly (they got one scene wrong where a small lunar lander is in free fall around the moon yet the passengers clearly experience acceleration), so I'm a bit curious to where in that movie you think it is shown wrong?

 

[Janus]

Thanks, but I believe that a spaceship in interplanetary or instellar flight would, in fact, have its propulsion system operating constantly. In fact, there have been some suggestions that one way to speed up long distance space flight would be to use a solar sail, accelerating the ship to higher and higher velocities. I doubt that an interstellar or even an interplanetary spaceship would make any progress without constant propulsion, at least until it began to achieve orbital insertion at its destination planet.
Louis

For interplanetary flight, the most energy efficient method is the Hohmann transfer orbit. You place the craft in an elliptical orbit around the Sun which just intersects the orbits of the launch planet and target planet. The only time you need to fire your engines is to insert the craft into the Hohmann transfer orbit, to perform a orbital inclination maneuver, and when you arrive at the target. Orbital mechanics takes over otherwise. This was the type of course the Discovery in 2001 was taking. (this is why the trip was so long that they put most of the crew in hibernation).

 

[LBrandt]

So what you're all saying is that for most interplanetary voyages, at least with present technology and propulsion systems, we would most likely just use acceleration for a short time, then coast until near target, then decelerate and orbit for landing. I would at least think that in the far future, when we have developed very efficient propulsion systems that might use simple and cheap power, that spaceships of that time would be under constant propulsion to shorten trip time, and therefore astronauts would NOT be able to do EVA during those periods. Would you agree with that?
Louis

 

[Ich]

So what you're all saying is that for most interplanetary voyages, at least with present technology and propulsion systems, we would most likely just use acceleration for a short time, then coast until near target, then decelerate and orbit for landing.

Yes, as long as the acceleration is not severely limited by the http://en.wikipedia.org/wiki/Ion_thruster" .

when we have developed very efficient propulsion systems that might use simple and cheap power, that spaceships of that time would be under constant propulsion to shorten trip time

Generally, to shorten trip time, you'd like to accelerate as quickly as possible. Only if acceleration is limited due to power constraints or payload resilience, you'll use extended acceleration phases. But I agree that this is the most likely scenario in the intermediate and far future.