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Two planets are separated by a distance of 4.5x108 m. One of the planets has a mass of 2.1x1021 kg. The force of attraction between the planets is 5x1024 N. What is the mass of the other planet? (Be careful with your algebra!)

Sagot :

facundo3141592

Answer:

The mass of the other planet is 7.23*10^(30) kg

Explanation:

For two objects of masses m₁ and m₂ respectively, separated by a distance r, the gravitational force between them is given by:

F = G*(m₁*m₂)/r^2

Where G = 6.67*10^(-11) m^3/(kg*s^2)

Here, we know that:

r = 4.5*10^8m

m₁ = 2.1*10^21 kg

F = 5*10^24 N

And we want to find the mass of the other planet, first, let's isolate m₂ in the force equation:

(F*r^2)/(G*m₁) = m₂

Now we can replace all the values that we know in the left side, and solve it:

m₂ =[(5*10^24 N)*( 4.5*10^8m)^2]/[6.67*10^(-11) m^3/(kg*s^2)*2.1*10^21 kg]

m₂ = 7.23*10^(30) kg

The mass of the other planet is 7.23*10^(30) kg

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