Could you calculate the mass of the planet?

[demode]

1. If you know the distance to a planet and the centripetal force on it, could you calculate the mass of the planet? Explain.
Fc = (MV^2) / (R)

I don't even know where to start; in the equation above, you can only substitute the known centripetal force in, but you can't substitute the distance to a planet or the velocity in.. Is there another equation or expression for centripetal force that would satisfy the two variables in the prompt?

 

[radou]

Hint: if you assume the planet is rotating around another one (which you can, since there exists a centripetal force), which is the other force which comes to your mind? (Hint 2: Newton's law of ___________)

 

[kyle8921]

Yes, there is another equation that can be used to calculate the mass of a planet given the distance to the planet and the centripetal force acting on it. This equation is known as the gravitational force equation, which is given by:

Fg = (GmM)/R^2

where G is the gravitational constant, m is the mass of the planet, M is the mass of the object orbiting the planet, and R is the distance between the two objects.

By setting the equations for centripetal force and gravitational force equal to each other, we can solve for the mass of the planet:

Fc = Fg

(MV^2)/R = (GmM)/R^2

Solving for m, we get:

m = (RV^2)/G

Therefore, by knowing the distance to the planet and the centripetal force acting on it, we can calculate the mass of the planet using the gravitational force equation. It is important to note that this equation assumes that the planet is a point mass, which may not be accurate for all planets. Additional factors such as the planet's density and shape may need to be considered for a more precise calculation.