Question

If the only force exerted on a star far from the center of the Galaxy (r = 7.40 ✕ 1020 m) is the gravitational force exerted by the ordinary matter (Mord = 1.90 ✕ 1041 kg), find the speed of the star. Assume a circular orbit and assume all the Galaxy's matter is concentrated at the center.

Answer 1

The value is
`v = 1.309*10^(5)\ m/s`

Step-by-step explanation:

The radius is
`r = 7.40 *10^(20) \  m`

The mass of the ordinary matter is
`M_(rod) =  1.90 *10^(41)\  kg`

Generally the speed of the star is mathematically represented as

`v = \sqrt{(G * M)/(r) }`

Here G is the gravitational constant with a value

`G = 6.67384 * 10^(-11)`

So

`v = \sqrt{(6.67384 * 10^(-11) * 1.90 *10^(41))/(7.40 *10^(20)) }`

=>
`v = 1.309*10^(5)\ m/s`