Find arc length given x = t sin t , y = t cos t and 0 ≤ t ≤ 1 ?

Question

Find arc length given       x    =    t          sin      t      ,       y    =    t          cos      t       and       0    ≤    t    ≤    1  ?

Lilly Maldonado · Accepted Answer

Given : mass of sun MSun =  2  ×      10          30        kg mass of earth MEarth=   6  ×      10          24       kg Average distance   r  =  1.5  ×      10    8   km                                =  1.5  ×      10    8    k  m  ×  1000  m      /    k  m                                =  1.5  ×      10          11        m According to the universal law of gravitation, F=G×MEarth×MSunr2 Plug in the given values to the formula,   F  =            6.67      ×              10                  −          11                    ×      6      ×              10                  24                    ×      2      ×              10                  30                            (      1.5      ×              10                  11                            )        2                F  =            6.67      ×      6      ×      2      ×              10                  (          −          11          +          24          +          30          )                            (      1.52      ×              10                  (          11          ×          2          )          )                        F  =            80.04      ×              10                  43                            2.25      ×              10                  22                        F  =  35.57  ×      10          (      43      −      22      )        =  35.57  ×      10          21          F  =  3.57  ×      10          22           N  .

The mass of sun is 2 xx 10^(30) kg and the mass of earth is 6 xx 10^(24) kg. If the average distance between the sun and the earth be 1.5 xx 10^8 km, calculate the force of gravitation between them.

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