In this paper we show that X-ray spectral observations of the ATHENA mission, which is planned to launch in 2031, can constrain the equation of state of superdense matter. We use our well-constrained continuum fitting method for mass and radius determination of the neutron star. Model spectra of the emission from a neutron star were calculated using the atmosphere code ATM24. In the next step, those models were fitted to a simulated spectra of the neutron star calculated for ATHENAs WFI detector, using the satellite calibration files. To simulate the spectra we assumed three different values of effective temperatures, surface gravities and gravitational redshifts. There cases are related to the three different neutron star masses and radii. This analysis allows us to demonstrate the precision of our method and demonstrate the need for a fast detector onboard of ATHENA. A large grid of theoretical spectra was calculated with various parameters and a hydrogen-helium-iron composition of solar proportion. These spectra were fitted to the simulated spectrum to estimate the precision of mass and radius determination. In each case, we obtained very precise mass and radius values with errors in the range 3--10% for mass and in the range 2--8% for radius within the 1-sigma confidence error. We show here that with the ATHENA WFI detector, such a determination could be used to constrain the equation of state of superdense neutron star matter.
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