Respuesta :
It will take the planet 16.69 minutes to complete one full orbit.
Data Given;
- r = 150*10^6km
- mass of star = 1.99*10^30kg
Gravitational Force
Applying gravitational and centripetal force
[tex]F = \frac{Gm_1m_2}{r^2}\\ F = \frac{mv^2}{r}\\ \frac{mv^2}{r}=\frac{Gm_1M2}{r^2}\\ v = \frac{2\pi r}{T} \\ \frac{m(2\pi r/T)^2}{r} = \frac{GM_1M_2}{r^2}\\ \frac{4\pi ^2r^2}{T^2} = \frac{GM}{r} \\ T^2 = \frac{4\pi^2 r^3}{Gm}\\ [/tex]
Let's substitute the values into the equation
[tex]T^2 = \frac{4\pi ^2 * (150*10^6)^3}{6.67*10^-11 * 1.99 *10^30}\\ T^2 = 1002799.605 \\ T = 1001.398s\\ T = \frac{1001.398}{60} = 16.69min [/tex]
It will take the planet 16.69 minutes to complete one full orbit.
Learn more on planetary rotation here;
https://brainly.com/question/21222010
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