Pat Dolan

2023-09-02 08:32:05 UTC

I would like to submit this little conundrum to this group for consideration:

Consider a distant observer traveling at .867 c ( gamma=2 ) relative to

the solar system along the line that is collinear with the sun's axis of

rotation. As the clockwork solar system spins beneath him, the distant

observer peers through his powerful telescope at Big Ben in London. In

accordance with special relativity, and after taking relativistic

doppler into account, the distant observer measures Big Ben's little

hand to make one revolution for every two revolutions of his own

wristwatch's little hand. He also observes that Big Ben's little hand

still makes 730.5 revolutions for every revolution that the earth makes

around the sun. From these two observations the distant observer

concludes that in his inertial frame of reference the earth's orbital

velocity is only half the velocity necessary to keep the earth in stable

orbit around the sun.

Will the earth spiral into the sun? If not, why not?

Note: Newtonian gravity is not assumed in this paradox. Invariant

spacetime curvature is assumed to be the cause of the earth's orbit

around the sun.

Consider a distant observer traveling at .867 c ( gamma=2 ) relative to

the solar system along the line that is collinear with the sun's axis of

rotation. As the clockwork solar system spins beneath him, the distant

observer peers through his powerful telescope at Big Ben in London. In

accordance with special relativity, and after taking relativistic

doppler into account, the distant observer measures Big Ben's little

hand to make one revolution for every two revolutions of his own

wristwatch's little hand. He also observes that Big Ben's little hand

still makes 730.5 revolutions for every revolution that the earth makes

around the sun. From these two observations the distant observer

concludes that in his inertial frame of reference the earth's orbital

velocity is only half the velocity necessary to keep the earth in stable

orbit around the sun.

Will the earth spiral into the sun? If not, why not?

Note: Newtonian gravity is not assumed in this paradox. Invariant

spacetime curvature is assumed to be the cause of the earth's orbit

around the sun.