If it travels at constant speec c in a straight line then you are in the vacuum and yes. In a gravitatory field (always are gravitatory fields but the size of the planets and energies that emits are too weak in this aspect to see a big difference with c, but in a gravitatory field light accelerates, with the limitation that v⩽c being v the velocity of light in the medium and c in the vacuum
You can think about law of gravtation of Newton, the equation is not the same, there are a development inr−2potencies if the body that generates the field is stopped ( if it is not stopped, the calculus could become very very complicated, there is no a general solution for the equation, and all the energy (not only masses) generate gravitational field. But even the field of the Sun in Solar System using Newtonian relativity but the mercury orbit is a very good aproximattion, even ignoring the field between planets, only every planet with the sun. That Mercury doesn´verify the orbit with the precission that we manage it, it is considered a proof of the gravity, that explain that being the nearest planet to the sun, the gravitational field is more intense. In the Earth, falling objects doesn´t need corrections for gravity but GPS measurements that are done seeing the time that pass since we send the signal to a satelitte and verifing the back time (with 3 satellites, I think there are 4 or more but for verification and possible correction of errors, theroetically can be done with 2 a geolocation). Then, if you measure a ray of light in a short surface, Spain size for example is a good aproximattion, like considering (this is not relativity, the world is spherical) that Spain is a plane is a good aproximattion but if you are doing a map of all the Earth, all the representations are not enough good neither for the human eye. Look in Internet, the version we use is Europe in the center and EEUU at the left, the representation we use reduce the size of Africa.
I have no links but it is very curious see the representations using another methods (it is a euclidean geometry even theorem that you can represent and spherical in a plane conserving distance between points). Well, sorry, I am extendinf very much, but be careful, when a physicist say that c is an universal constant and is the light veloicity is an abrevviation, a good abreviation in many practical cases, but c is the light velocity in the vacuum, in a gravitational field neither (or any other 0 rest mass particle that carry the same velocity) can be 0 but an instant selecting a coordinate system local and causal ) is exctriclty c, they are THE VARIATIONS of the gravitational field that changes his velocity. The only certain is that the modul is <c, neither straight neihter <c is possible. More than this, it depends totally from the gravitational field for the electromagnetic field (and the visible range of it, the light)