逕向加速度關係是星系中可見物質和總加速度間的關係。在文獻中，逕向加速度關係一般在旋渦星系中量測，而較少在橢圓星系中探討。學習橢圓星系中的逕向加速度關係是很重要，可以明瞭全部的星系是否在修改牛頓力學(MOND)中有一個加速度常數。在這份工作，分別從史隆數位巡天、UPenn列表、ATLAS\textsuperscript{3D}中篩選了1266、4195、以及159個橢圓星系。其中的總加速度是由觀測中速度離散度中推演出。因為橢圓星系是壓力支撐系統，推演的加速度仰賴模型本身。赫恩奎斯特(Hernquist)模型被使用在橢圓星系的可見物質，同時也使用在暗物質模型和修改牛頓力學中。逕向加速度關係在史隆數位巡天的資料是計算在有效半徑上，而在ATLAS\textsuperscript{3D}中則是考量在多個半徑上。不同模型的結果也有所比較，包含修改牛頓力學的特徵加速度$a_0$。史隆數位巡天的樣本中計算出$a_0=4.61\times 10^{-10} m/s^{2}$，而UPenn得出$a_0=3.76\times 10^{-10} m/s^{2}$，ATLAS\textsuperscript{3D}則得出$a_0=8.23\times 10^{-10} m/s^{2}$。基於這個結果，橢圓星系看似是旋渦星系往牛頓力學區域的延伸，但顯示了不同的斜率。這也許是因為橢圓星系的模型依賴性所導致的。;Radial Acceleration Relation (RAR) is a relation between the baryonic, and total acceleration of a galaxy. RAR is typically measured on spiral galaxies in literature, so fewer studies have focused on elliptical galaxies. It is important to study the RAR of elliptical galaxies in order to find out whether all galaxies shift towards MOND with a constant acceleration scale. In this work, data of 1266, 4195, and 159 elliptical galaxies were selected from SDSS DR15, UPenn catalog, and ATLAS\textsuperscript{3D} respectively. Each of their total accelerations were deduced from their measured velocity dispersion. Since elliptical galaxies are pressure-supported systems, the deduced acceleration depends on the model used. Hernquist model is used for the luminous (or baryonic) part of the elliptical galaxies, and also for both dark matter halo and in Modified Newtonian Dynamics (MOND). The RAR of the SDSS samples were obtained at their effective radius, while the ATLAS\textsuperscript{3D} RARs were obtained at multiple binned radii. The results from different models are then compared, including the MOND characteristic acceleration scale $a_0$. A value of $a_0 = \lsqSDSSao \times 10^{-10}$ $\nicefrac{m}{s^2}$ was calculated from the SDSS samples, $a_0 = \lsqUPao \times 10^{-10}$ $\nicefrac{m}{s^2}$ from UPenn, and $a_0 = \lsqAtlasao \times 10^{-10}$ $\nicefrac{m}{s^2}$ from ATLAS\textsuperscript{3D}. Based on the results, the elliptical galaxies seem to be a continuation of the spiral galaxies towards Newtonian Dynamics regime, but they follow a different slope. This may be due to the model dependency of elliptical galaxies.
