A newly discovered planet is found to have density 2/3 ρe and radius 2r , where ρe and re are the density and radius of earth, respectively. the surface gravitational field of the planet is most nearly
The surface gravitational field of the planet can be calculated using formula: [tex]g= \frac{G*m}{ r^{2} } [/tex] Where: G=gravitational constant m=mass of planet r=radius of planet
For Earth this gives: [tex]g= \frac{G* m_{E} }{( r_{E})^{2} } \\ \\ g= \frac{G* \rho_{E}* \frac{4}{3} * ( r_{E} )^{3}* \pi }{( r_{E})^{2}} \\ \\ g= {G* \rho_{E}* \frac{4}{3} * ( r_{E} ) * \pi }[/tex] Before we calculate gravitational field of a planet we need to calculate it's mass. It can be calculated using density. [tex]\rho= \frac{m}{V} \\ m=\rho*V \\ m= \frac{2}{3} * \rho_{E} * \frac{4}{3} * (2r_E} )^{3} * \pi \\ \\ m= \frac{8}{3}* \rho_{E} * (2r_E} )^{3} * \pi [/tex] Gravitational field of a planet is: [tex]g= \frac{G* \frac{8}{3}* \rho_{E} * ( 2r_{E} )^{3} * \pi }{( 2r_{E})^{2} } \\ \\g= \frac{16}{3}*G*\rho_{E}*r_{E}* \pi[/tex] Now we compare Earth's and planet's gravitational fields: [tex]{G* \rho_{E}* \frac{4}{3} * ( r_{E} ) * \pi }.....................\frac{16}{3}*G*\rho_{E}*r_{E}* \pi \\ \\1.....................4[/tex]
Gravitational field on a planet is 4 times greater than gravitational field on Earth.
