Do M\"arzke-Wheeler effects influence on measured data in nature?

We wonder whether M\"arzke-Wheeler effects influence on measured data in nature. Through a formula developed in this letter for the calculation of the M\"arzke-Wheeler map of a general accelerated observer, we study the influence of the M\"arzke-Wheeler acceleration effect on the NASA's Pioneer anomaly and found that it is about a fifth of the anomaly value. Due to statistical errors in the measured anomaly, it is not possible to neither confirm nor neglect the influence of the M\"arzke-Wheeler acceleration effect on the measured Pioneer data. We hope that the ideas presented here could encourage other research teams in the search for other observational objects that could finally answer the question posed in this letter.