contestada

The planet zeta has 2 times the gravitational field strength and sane mass as the earth , how does the radius of zeta compare with the radius of the earth

Respuesta :

Gravitational field strength is given by the formula

[tex]g = \frac{GM}{R^2}[/tex]

now another planet Zeta is of same mass but double the gravitational strength

[tex]2g = \frac{GM}{r^2}[/tex]

now plug in the value of g from above

[tex]2\frac{GM}{R^2} = \frac{GM}{r^2}[/tex]

by solving above equation for radius "r"

[tex]r = \frac{R}{\sqrt2}[/tex]

so its radius is 0.707R

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