Summary: A photon exchanges momentum as it bypasses a large gravitational well during transit. The photon experiences a change in momentum and its path is bent as it interacts with the gravitational field. A photon simultaneously gains and loses momentum (p) from a gravitational interaction with a massive object. However, a photon maintains its relative path with speed c and covers the same distance (d) as compared to its constant speed. The curvature of the photon's path is understood in terms of the exchange of momentum experienced by the photon.
Relevant equations: p = E/c, constant = c = 299792458 m/s, distance = (speed x time) = (c m/s * s)
Bending of the travelling path of a body when its speed is unchanged: - photon, spacecraft:
The bending of photon's path is due to it's constant speed @c but it's increased energy and frequency corresponding to the increased gravitational influence on it.
Since photons speed is constant, an incremental change in it's energy and/or frequency makes the photon change it's path bent.
It's like gravity assist (sling shot) by a massive planetary body to a bypassing spacecraft in a condition when the speed of the spacecraft remains unchanged but its path bends as its kinetic energy increases.
What happens in the background:
When the photon maintains a constant speed @c, and increases its Energy, it is bound to increase its frequency too. Such increased frequency, at its constant speed, does not allow the photon to maintain a straight path anymore, as the gained frequency deviates the photon path from its apparent straight path to a bent path until the the photon reaches its earlier frequency.
The gain of its energy is temporary - temporarily synchronised. Photon frequency synchronised with gravitational field - transfers energy to the photon.
So (E'-E) deviates the path of the photon and bends, since the photon cannot increase it's constant speed, it bends.
Note: The momentum of a photon is directly proportional to its frequency and inversely proportional to its wavelength. Photons momentum is given by p=hλ, where λ is the photon wavelength. Photon energy and momentum are related by p=Ec , where E=hf=hcλ for a photon
#gravityassist #slingshot #increadedenergy #increasedfrequency
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