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Two identical planets, each with a mass of 1024 kg, orbit around the midpoint between the two planets. If the distance between the two planets is 2 x 108 m (as measured from their centers), how fast is each of the planets moving in their orbit?

Respuesta :

Answer:

each of the planets moving  = 408.35 m/s

Explanation:

given data

mass =  [tex]10^{24}[/tex] kg

distance between two planets = 2 × [tex]10^{8}[/tex] m

solution

if distance between two planet is 2 × [tex]10^{8}[/tex] m it mean it's diameter so

that radius will be 1 × [tex]10^{8}[/tex] m

and

F = [tex]\frac{G*m*m}{2r^2}[/tex]    ................1

and

F = [tex]\frac{m*v^2}{r}[/tex]   ..............2

so from equation 1 and 2 will be

[tex]\frac{G*m*m}{2r^2}[/tex] =  [tex]\frac{m*v^2}{r}[/tex]  

v = [tex]\sqrt{\frac{G*m}{4*r}}[/tex]     ............2

put here value

v = [tex]\sqrt{\frac{6.67*10^{-11}*10^{24}}{4*10^8}[/tex]    

v = 408.35 m/s

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