A photon is emitted in a vacuum some arbitrary distance above a spatially isolated  spherical mass equal to Earth. The photon is emitted in a parallel direction to the surface.  Will the photon orbit at the same height continuously, fall to Earth or just continue out along an increasingly flat space/geodesic?

Edited January 18Jan 18 by StringJunky

The trajectory would depend on the mentioned distance and on the mass rotation.

It would not orbit, as there’s not enough mass (or, more precisely, density). A photon will orbit at a distance of the photon sphere, which is 3/2 the Schwarzschild radius for a non-rotating mass. For a rotating mass, as Genady said, it would depend on the rotation, and whether you emit with a velocity component in the direction of rotation or opposite

For the earth, the Schwarzschild radius is much smaller than the physical radius, so orbits are not possible. There would be a very slight deflection toward the earth as the photon went out into space. Even around the sun the deflection of a tangential photon would be small, as Eddington confirmed.

 

3 hours ago, swansont said:

It would not orbit, as there’s not enough mass (or, more precisely, density). A photon will orbit at a distance of the photon sphere, which is 3/2 the Schwarzschild radius for a non-rotating mass. For a rotating mass, as Genady said, it would depend on the rotation, and whether you emit with a velocity component in the direction of rotation or opposite

For the earth, the Schwarzschild radius is much smaller than the physical radius, so orbits are not possible. There would be a very slight deflection toward the earth as the photon went out into space. Even around the sun the deflection of a tangential photon would be small, as Eddington confirmed.

 

Thanks. So an extremely high density is necessary for this scenario, so that the physical radius is smaller than the Schwarzschild radius to allow a photon to orbit? Are their bodies in the universe that have the required mass/density properties to confine a photon to its orbit, in principle? 

I'm trying to get an idea of the mass/density necessary to confine a photon some uniform orbital distance from a body

Edited January 18Jan 18 by StringJunky

2 hours ago, StringJunky said:

Thanks. So an extremely high density is necessary for this scenario, so that the physical radius is smaller than the Schwarzschild radius to allow a photon to orbit? Are their bodies in the universe that have the required mass/density properties to confine a photon to its orbit, in principle? 

Black holes, and possibly some neutron stars

40 minutes ago, swansont said:

Black holes, and possibly some neutron stars

Thanks.

e.g. Photon Sphere?

https://en.wikipedia.org/wiki/Photon_sphere

 

(I'd think if anything as small as Earth could have an effect like this, it'd be very obvious. I doubt we'd be seeing the stars at night, just a smear of light.)

14 hours ago, StringJunky said:

I'm trying to get an idea of the mass/density necessary to confine a photon some uniform orbital distance from a body

Note that such photon orbits would be unstable, ie any small perturbation would lead to the photon to either in-spiral, or escape to infinity. This is because these orbits are on a local maximum of the effective potential function for the photon. This is true for all four basic BH types.

Whether it is possible to construct a more complicated spacetime in which stable photon orbits can exist, is an interesting question; I don’t immediately know the answer to that.