# Was Feynman right about the chalk in the spaceship?

I have heard this problem many times before from various sources, but I am quoting Feynman's words from his Lectures On Physics (Vol : 1) , just in case you want it to be authentic.

Therefore, Gagarin or Titov would find things weightless inside spaceship; if they happened to let go of a piece of chalk, for example, it would go around the earth in exactly the same way as the whole spaceship, and so it would appear to remain suspended before them in space.

This is true if the chalk was suspended along the spaceship's orbit. What if it is not?

Wouldn't the chalk lack the velocity necessary for the lower orbit and spiral inwards? It would no longer be stationary for the cosmonaut.

Or, does the gravitational pull due to the spaceship cancel out the excess force on the chalk by the earth?

• Absent atmospheric effect it would certainly not "spiral inwards", but would be in a slightly different orbit. But part of the problem here is scale. In your drawing the difference in radial position of the chalk and ship comes to something like a tenth of either value, while Feynman was thinking of a case where that difference was at the parts-in-a-million level or less. For a detailed description of the small effects present in Feyman's case I would look for the Robert Forward article on microgravity in orbit. – dmckee Jul 21 '18 at 17:54

You are right; the chalk will continue on an orbit that is consistent with its initial position and velocity when it is released. But it will not move in a spiral. The gravitational attraction of the spacecraft can be ignored.

To begin, take note that objects in higher circular orbits move more slowly than objects in lower circular orbits.

Now assume, for example, that the spacecraft is cigar-shaped, and keeps one end (the "low end" always pointed toward the center of the earth (the way the Moon always keeps one face toward the earth). Let's call the other end the "high end". And, let's assume that the spacecraft is in a circular orbit.

In the same orbit as the spacecraft, place a cigar-shaped column of loose chalk pieces, distributed from a "low end" to a "high end" of the column. The chalk pieces are all initially moving at the same velocities in their orbits as the corresponding parts of the spacecraft.

Now push the "start" button and watch what happens. The spacecraft keeps going in its circular orbit. The column of chalk pieces, however, begins to stretch.

The pieces at the high end are moving too fast to be in a circular orbit at their initial distance from Earth, so they initially move gradually a bit farther from the Earth, losing a bit of speed, until they're halfway around the Earth, at which point they begin to drop gradually closer to the Earth, gaining speed, coming back to their starting point moving at the same initial velocity. Their orbit is slightly ellipsoid rather than circular, and is longer than the spacecraft's orbit. It is also moving on the average slightly slower than the spacecraft.

The pieces at the low end are moving too slow to be in a circular orbit, so they begin to drop closer to the Earth, gaining speed. Halfway around the Earth they reach a maximum speed then start rising while losing speed, and eventually come back to their starting point at the same initial velocity. Their orbit is slightly ellipsoid, too, but is shorter than the spacecraft's orbit; and they move on the average slightly faster than the spacecraft.

So, the low end pieces get back to their starting positions before the high end pieces do. The initial cigar-shaped distribution of chalk pieces is therefore stretched, with the low end pulled forward (in the direction of orbital velocity) and the high end pulled backward.

• Deleted my answer in favor of your more thorough one, but I'd just like to point out that if you attempt the experiment inside a spaceship that has a breathable atmosphere and, has a ventilation system that keeps the air breathable, then the circulating air will totally invalidate the experimental results. – Solomon Slow Jul 21 '18 at 18:04
• That's a good point. Also, electrostatic voltage differences between the chalk piece and the spacecraft could have a substantial effect. Feynman would have quickly agreed that all the above is correct, and made the clarification that for all practical purposes the chalk and the spacecraft follow the same trajectory if their centers of mass are close together and if the chalk is initially at rest relative to the spacecraft. He was conveying the concept of an "inertial frame", which in reality comprises only an infinitesimal volume. – S. McGrew Jul 21 '18 at 18:52