Am I missing something here?  As the spaceship can go lots faster, and assuming it can approach as close as it likes and manoeuver freely, what's to stop it just following inhabitant about.

If my assumptions are not valid, then you'll have to tell me the limits.

Assuming that the inhabitant doesn't want to be seen, I've found a way the spaceship can move so to always spot the inhabitant. This gives the lower limit for v/u in this case. I would like to hear your opinion on it. Here it goes...

Set up a spherical coordinate system with the origin at the center of the planet. Let the spaceship be at the distance

from the center of the planet, with angular coordinates

and

. If the spaceship is point A and the origin is point O, draw a tangent from the spaceship to the planet and call it point B on the planet - there are two of these, any one will do. Now, denote the angle AOB by

. Since BOA is a right angle, we have

. Now, let the ship circle around the z-axis with the velocity

. The time it takes for one complete revolution is

. At the same time the ship sweep the strip of the planet of width

. So, in order to see the inhabinant, it has to go through all the strips taking care that the inhabitant cannot escape, i.e. the time neccesary for him to cross the strip

should be greater or equal to the time of revolution. So

. Using the relation above, one has

. Since the relation must hold for all

, we take the worst case scenario

. Then the only free parameter is

and we can choose it so to minimize the left hand side of the inequality. Numerically, one gets

.

Does this look ok?

Hi all;

I have you beat, I have been missing the point here since post #3. If you are trying to set up some type of pursuit curve, I don't know if you defined the problem enough. It seems to me that this condition exists:

If the sphere is very small and spaceship very far away, then no matter which direction the spaceship maneuvers, to the sphere it will appear stationary. The inhabitant may then get around to the other side of the sphere.

Say the ship is 100 000 u away and travels at a speed of 10 u. The sphere has a circumferences of 1 u and the inhabitant travels at a speed of 1 u. I think the inhabitant can duck on the other side of the sphere.