Spaceship arriving at a planet

[norvegicusbas]

Hello.
Me and a friend of mine were trying to get our heads around a few of the paradoxes that are found within Einstein's theory of relativity and he came up with something we could not work out ( though I am sure someone here will be able to :)

Imagine you were in a spaceship traveling at the speed of light towards a distant planet. This planet is very dark and the spaceship needs to put on its headlights to see exactly where this planet is. Soon as the headlights are switched on all those aboard the spaceship ( according to their reference frame ) see the light from the headlights shine off into the blackness of space at the speed of light and strike the planet. With the planet well lit from the spaceships headlights the ship continues to approach for an eventual landing. But what will the people on the planets surface see? Do they see the light from the headlights arriving at a point in time before the arrival of the spaceship?

 

[Passionflower]

The light from the headlights of the spaceship will always arrive before the spaceship arrives. The spaceship can (at least hypothetically) approach the planet with a speed almost the speed of light but it can never reach the speed of light.

 

[norvegicusbas]

The light from the headlights of the spaceship will always arrive before the spaceship arrives. The spaceship can (at least hypothetically) approach the planet with a speed almost the speed of light but it can never reach the speed of light.

Thankyou Passionflower for your quick reply.
What would the outcome be though if the spaceship was made by some incredibly advanced alien race and could be constructed ( along with the passengers ) from a massless material?

 

[Passionflower]

Thankyou Passionflower for your quick reply.
What would the outcome be though if the spaceship was made by some incredibly advanced alien race and could be constructed ( along with the passengers ) from a massless material?

Well in that case it could never slow down and was doomed forever to travel at the speed of light. But clearly you must understand there is no such material.

 

[JesseM]

Thankyou Passionflower for your quick reply.
What would the outcome be though if the spaceship was made by some incredibly advanced alien race and could be constructed ( along with the passengers ) from a massless material?

In that case the ship does not have its own inertial rest frame, so it is no longer true that the light from the headlights must move at c in the frame of the ship.