Calculating Speed and Time of Nolan Ryan's Baseball Orbit on the Moon

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To calculate the speed at which Nolan Ryan must throw a baseball to achieve a circular orbit on the moon, the correct formula involves gravitational parameters rather than V = G*R. The gravitational force acting on the baseball must equal the centripetal force required for circular motion. The correct orbital speed can be derived from the equation V = sqrt(G * mm / rm), where mm is the moon's mass and rm is its radius. The time taken to complete one orbit can be calculated using T = 2πrm / V. Proper understanding of satellite motion and gravitational equations is essential for accurate calculations.
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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 mm = 7.35×(10*22power kg), and its radius is rm = 1740 km. The gravitation constant G = 6.67×10(-11power) Nm2/kg2.

a) Find the speed at which Nolan must throw the ball for such a circular orbit? V= ms

(b) How long (in hours) does the ball take to complete one orbit? T= hrs


is the equation V=G*R? if so i used 7.35*10to the 22nd power * 6.67 *10 to -11 power?
i got 4.90245e12, and it said i was wrong.



The Attempt at a Solution

 
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but i can't figure out the equation for B
 


did i do A right?
 


JJ89 said:
is the equation V=G*R? if so i used 7.35*10to the 22nd power * 6.67 *10 to -11 power?
i got 4.90245e12, and it said i was wrong.
No, the equation is not V = G*R. Look up the correct equation for satellite motion in a circular orbit in your textbook. You can also derive it using Newton's Second Law combined with Newton's Law of gravitation.
 

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