Suppose that Nolan Ryan stands on the surface of the moon and throws a baseball

Question

Suppose that Nolan Ryan stands on the surface of the moon and throws a baseball horizontally. If the baseball has a high enough speed and does not strike any mountain, it can orbit around the moon and, after completing the orbit, strike Nolan from behind. The mass of the moon is m m = 7.35 times l022 kg, and its radius is I m = 1740 km. The gravitation constant G = 6.67 times l0 - 11 Nm2/kg2. Find the speed at which Nolan must throw the ball for such a circular orbit. (b) How long (in hours) does the ball take to complete one orbit?

Explanation / Answer

arad=v2/r Mball*a=F=G*Mmoon*Mball/r2 use these two formulas together to solve for v. We canfind arad (radial acceleration) by the secondequation, and we were given r as 1740km. In the second equation, we set Newtons F=ma to the equationfor the force of gravity, also from Mr. Newton. Notice howthe mass of the ball cancels out, it appears on both sides of theequation, we can divide it off of both sides. G, r and themass of the moon are given. a=6.67*10-11*7.35*1022/(1740*1000)2  Notice we converted km to m. solving, a =1.619m/s2       Notice thismakes sense, it's less than the 9.8m/s2 we feel on theearth, as we expect and google confirms! using this a value in the first equation give us (1.619)*(1740*1000)=v2 v=1687.54 m/s solving the second part is easy, we know the circumference is2Pi*r so the total distance is 10.9*106 meters. distance / velocity gives us time so,10.9*106/1687.54=total time = 6478.5 Units are in seconds! convert to hours and you're done! BTW, Nolan Ryan used to be my hero, but I doubt he could throwthat fast anymore, even on the moon! v=1687.54 m/s solving the second part is easy, we know the circumference is2Pi*r so the total distance is 10.9*106 meters. distance / velocity gives us time so,10.9*106/1687.54=total time = 6478.5 Units are in seconds! convert to hours and you're done! BTW, Nolan Ryan used to be my hero, but I doubt he could throwthat fast anymore, even on the moon!

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