# Does gravity accelerate you towards the geodesic of light between you and the mass?

If there's a planet far away, you will accelerate straight towards it due to gravity. If you place a Schwarzschild black hole right in the middle between you and the planet (the distance between the black hole and the planet remains constant), you will see a ring around the black hole from the light of the planet. That light takes a longer path to reach you than before.

a) Even though you will accelerate faster in that direction due to the added black hole's gravity, is the gravitational effect exclusively due to the planet now smaller than before because the shortest path for light is longer?

b) As you approach the event horizon, light coming from all direction including the other side of the black hole increasingly travels inwards, towards the black hole. As you get really close to the event horizon, does that mean the gravity of the planet is actually contributing to attracting you in the outwards direction, even if it's on the other side of the black hole from you?

• To see how gravity behaves, you need to understand what it is. Gravity is caused by a gradient of the time dilation. If you are in the living room, but time in your bedroom runs a tiny fraction of a percent slower, then you’d be violently thrown by gravity from the living room to the bedroom. In your setup, think of how the time dilation caused by the planet adds to the one caused by the black hole and see what it does to the gradient. Commented Jul 10 at 3:28
• You are essentially asking if the gravitational acceleration (a.k.a. static gravity) follows lightlike geodesics. This is not the case, at least not always. For example, the Earth is attracted to the Sun in the direction of its actual position, but not in the direction where we see it in the sky 8 minutes behind (or 4 diameters of the Sun). So not in the direction of lightlike geodesics. See this question for more info (although no good answers there): physics.stackexchange.com/questions/492870 Commented Jul 10 at 3:38