A deep-space satellite is sent to orbit a distant planet with unknown mass. On
arrival, the satellite begins its orbit and measures a gravitational pull from the
planet of 620 N. If the satellite has a mass of 450 kg and orbits the planet at a
radius of 4.0 x 10^6m, what is the approximate mass of the planet?(recall that G=6.7x10^-11 N•m2/kg^2.)

Respuesta :

Answer:

The mass of the planet is [tex]3.29\times 10^{23}\ kg[/tex].

Explanation:

Given that,

The gravitational pull on the planet is 620 N

Mass of a satellite is, m₁ = 450 kg

Radius of a planet is [tex]4\times 10^6\ m[/tex]

We need to find the mass of the planet. Gravitational force is given by :

[tex]F=\dfrac{Gm_1m_2}{r^2}[/tex][tex]m_2[/tex] is the mass of the planet

[tex]m_2=\dfrac{Fr^2}{Gm_1}\\\\m_2=\dfrac{620\times (4\times 10^6)^2}{6.7\times 10^{-11}\times 450}\\\\m_2=3.29\times 10^{23}\ kg[/tex]

So, the mass of the planet is [tex]3.29\times 10^{23}\ kg[/tex].

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