Question

Between the orbits of Mars and Jupiter, several thousand small objects called asteroids move in nearly circular orbits around the Sun. Consider an asteroid that is spherically shaped with radius r and density 2000 kg/m^3.

1. You find yourself on the surface of this asteroid and throw a baseball at a speed of 24 m/s. If the baseball is to travel around the asteroid in a circular orbit, what is the largest radius asteroid on which you are capable of accomplishing this feat?

Answer 1

The radius is
`r = 3.21*10^(4) \ m`

Step-by-step explanation:

From the question we are told that

The density is
`\rho = 2000 \ kg/m^3`

The speed is
`v = 24 \ m/s`

Generally the largest radius of the asteroid is mathematically represented as

`r = \frac{v^2}{ \sqrt{G * \rho * [(4)/(3) ] * \pi} }`

=>
`r = \frac{24^2}{ \sqrt{ 6.67*10^(-11) * 2000 * [(4)/(3) ] *3.142 } }`

=>
`r = 3.21*10^(4) \ m`