If we witness events occurring on the Moon, where gravitation is weaker than on Earth, would we expect to see a gravitational red shift or a gravitational blue shift? Explain.
Solution 17E Introduction If the frequency of electromagnetic radiation originates from a source which is in a gravitational field reduces, there will be a gravitational redshift for the electromagnetic radiation. Similarly, if the frequency of electromagnetic radiation originates from a source which is in a gravitational force field increases, there will be a gravitational blueshift for the electromagnetic radiation. Step 1 Here, they have provided that, the event is happening in moon. The gravitational force is weak at moon while comparing it with the earth. So, we should consider the time dilation factor to discuss about the change in frequency of the event. The gravitational time dilation is the time elapsed between two events as seen by the observer situated at different frames in which the influence of gravitational forces are different. The time dilation in weak gravitational field is greater than that of strong gravitational field. It means, the clock ticking in weaker gravitational field will run faster than that of the same clock in stronger gravitational field. So, as the waves travel from moon to earth, the gravitational force will increase. So, the time elapsed will be more since it is travelling from weaker field to stronger field. We know that, the frequency is inversely proportional to time. That is, frequency, f 1/T Therefore, as time elapsed increases, the frequency decreases. Here, the time elapsed is more as per the time dilation principle. So, the frequency will be reduced and gravitational redshift will occur. Conclusion The frequency will be decreased as the wave travels from moon to earth. Hence gravitational redshift will occur.
