There is no scientific method that can prove the actual and true age of the earth. Scientists, however, have projected the age of the planet by doing calculations and analysis. These calculations often involve some assumptions. 
One of the assumptions is that the processes that happen on earth happen at the same rate that they did back then. For example, finding out the age of the planet is done by observing the rate at which erosion of rocks happen and assuming that the rate has been constant from the start of time. 

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Secondly, the earth was formed out of molten rocks. Scientists like William Thomson calculated the time that it would take for molten rock to cool into its current temperature. Charles Darwin was a biologist who claimed that the age of planet earth can be calculated by using the molecular clock. 

He assumed that the genetic dispersion happens at the same rate. He looks at the rate of dispersion of species and dates back to the bacteria which were the earliest ancestor of the organisms that are on the Earth. 

The fourth assumption is that both the moon and the earth broke apart from molten rock. This dating of the earth can be done by calculating the number of years for this impact to give earth its rotation speed and its 24 hour day. The experts also carry out calculations on how fast the ocean has accumulated salt from erosion and assuming that the rate is constant. Other scientists have studied the fossils and concluded that from their high elevation the earth was once covered with water and they calculate the time that it takes for water to evaporate to its current sea levels.