Just a quick question about gravitational constant of a planet. The Grav F is deemed to be F=GM(earth)m(planet)/r^2. If you have a planet that is 2x as large (2x Rearth and 2x Mass Earth) What would it's Grav Constant be? So the way I understand it is that f=mg and we substitute that in to the grav force equation described earlier, which gives us g=GMearth/r^2. Therefore, the equation states that the grav force doesnt depend on the other planet's mass. So wouldn't the G force on that planet be .25g? But that's apparently not the case. The answer was .5g. Why do we still consider the mass of the planet?
Gravitational Constant of Unknwn Planet
- Thread starter Ehwic
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Not exactly. Think of it like this, rather than comparing two planets:
F = G(Mplanet)(Mobject)/r^2
In F = Ma
The "M" stands for the object. Therefore, the mass of the planet should be in the acceleration, or gravity.
So...
g = GMplanet/r^2
Therefore, when computing the gravitational constant of a specific planet, you do include the mass of that planet you're measuring. In the way you were doing it, you were using the mass of the "object" (earth) in your equation. But in reality, every planet's gravitational constant is not based off of Earth. Instead, each planet's constant is found individually, so we use the mass of that specific planet.
F = G(Mplanet)(Mobject)/r^2
In F = Ma
The "M" stands for the object. Therefore, the mass of the planet should be in the acceleration, or gravity.
So...
g = GMplanet/r^2
Therefore, when computing the gravitational constant of a specific planet, you do include the mass of that planet you're measuring. In the way you were doing it, you were using the mass of the "object" (earth) in your equation. But in reality, every planet's gravitational constant is not based off of Earth. Instead, each planet's constant is found individually, so we use the mass of that specific planet.
D
deleted393595
1) Universal Gravitational Constant would always be the same.
2) Set it up like this:
M (object) a=G * M(planet) * M(object)/r^2
The mass of the object will cancel out on both sides.
Plug in (2*M(earth)) for the mass of the planet above, and (Radius x2), and you'll end up getting 0.5 for acceleration.
