# Time dilation between perihelion and aphelion of earth with the combined effects of Special Relativity and General Relativity

I am a high school student and a total newbie in the field so I apologize for any misconceptions or mistakes I may do in advance.

I am trying to calculate the time dilation observed on earth at it's aphelion state by an observer on earth at it's perihelion state.

I thought because earth's movements must be parallel to each other at those states their velocities can be added to find their relative velocity to calculate time dilation predicted by special relativity with the formula: $$t'=\frac{t}{\sqrt{1-\frac{v ^2}{c^2}}}$$

And that I can use $$t_0=t_f\sqrt{1- \frac{2GM}{rc^2}}$$ for both situations to form a ratio between the time dilations predicted by general relativity for these situations.

And finally add them up to find the overall time dilation observed in earth's aphelion state by an observer on earth on its perihelion state.

However, I have also seen that the Schwarzschild metric is used in an answer to a very similar question by Mr. John Rennie: Does Earth experience any significant, measurable time dilation at perihelion?

Is my method correct or should I use the Schwarzschild metric to answer the question? If the latter, does this include the effects of time dilation related with Special Relativity? If not, can these effects be combined together by simply adding them, or is there another method to do this?

• A sloth is 10 times slower than an average mammal. A sloth in a spaceship moving at 0.87 c is 20 times slower than a normal mammal. 10*2=20. You multiply slowness factors, you don't add them. Jan 10, 2021 at 10:35