On October 24, my country's first lunar exploration satellite, Chang'e-1, was successfully launched. On November 5, it entered a lunar orbit near the moon at an altitude of about 200 kilometers, and began its scientific exploration around the moon for a period of one week or one year. It is known that the Chang’e-1 satellite orbits the moon at an average speed of 2.5 kilometers per second, and it takes 127 minutes to orbit the moon. However, since the moon is the earth’s satellite, it is also orbiting the earth at a certain speed. If various factors are deducted, Chang’e-1 It takes only about 78 minutes for the satellite to rotate around the stationary moon. We know that the diameter of the moon is approximately equivalent to (14/51) the diameter of the earth's equator. What is the approximate radius of the Earth at the equator? (The orbit is regarded as a circle, the moon is regarded as a circle, π=3)
10月24日我国首颗探月卫星嫦娥1号发送成功，已于11月5日进入近月球约200千米高度的绕月轨道，开始为期一周大约一年的绕月科学探测．已知嫦娥1号卫星绕月速度平均每秒是2.5千米，绕月一周需127分钟，但是由于月球是地球的卫星，也在按一定的速度绕地球转动，如果扣除各种因素，嫦娥1号卫星绕静止的月球转动，则大约只需要78分钟．我们知道，月球的直径大约相当于地球赤道直径的(14/51)．地球的赤道半径大约是多少千米？(轨道视为圆形，月球视为圆形，π=3)
<gadget id="calculator">1_750 * 2</gadget>
<output>3_500</output>

<gadget id="calculator">14 / 51</gadget>
<output>14/51 = around 0.27451</output>

<gadget id="calculator">3_500 / (14/51)</gadget>
<output>12_750</output>

<gadget id="calculator">12_750 / 2</gadget>
<output>6_375</output>

<result>6_375</result>