A recently discovered planet has a mass twice as great as Earth's and a radius twice as large as Earth's. What will be the approximate size of its gravitational field?
Apparently it isn't 2 * 9.8...
2m/4r^2
1/2 * g
4.9
To determine the approximate size of the gravitational field on the recently discovered planet, we can use the formula for the gravitational field strength:
g = G * (M / r^2)
Where:
g is the gravitational field strength,
G is the gravitational constant (approximately 6.67430 × 10^-11 N m^2/kg^2),
M is the mass of the planet, and
r is the radius of the planet.
Given that the recently discovered planet has a mass twice as great as Earth's (M = 2 * M_Earth) and a radius twice as large as Earth's (r = 2 * r_Earth), let's substitute these values into the formula:
g = G * ((2 * M_Earth) / (2 * r_Earth)^2)
Simplifying further:
g = G * (2 * M_Earth) / (4 * r_Earth^2)
g = (G * M_Earth) / (2 * r_Earth^2)
From the equation, we see that the gravitational field strength on the newly discovered planet will be half as strong as on Earth (assuming the mass and radius of Earth are denoted as M_Earth and r_Earth, respectively).
Therefore, the approximate size of its gravitational field will be approximately half of Earth's gravitational field strength, which is about 4.9 m/s^2.
To determine the approximate size of the gravitational field of the recently discovered planet, we can use the formula for gravitational field strength:
gravitational field strength = (gravitational constant * mass of the planet) / (radius of the planet)^2
The gravitational constant, denoted by G, is a universal constant equal to 6.67430 × 10^-11 N(m/kg)^2. The mass of the planet is twice the mass of Earth, and the radius of the planet is twice the radius of Earth.
Let's denote the mass of Earth as M and the radius of Earth as R. The mass of the recently discovered planet would then be 2M, and the radius would be 2R.
Plugging these values into the formula, we have:
gravitational field strength = (G * 2M) / (2R)^2
However, we can simplify this expression further. Since the radius is squared in the denominator, when we have a ratio of radii, that ratio squared will cancel out:
gravitational field strength = (G * 2M) / 4R^2
Simplifying further:
gravitational field strength = (1/2) * (G * M) / R^2
Here we can observe that the gravitational field strength is not directly proportional to the mass or radius of the planet, but indirectly proportional to the mass and inversely proportional to the square of the radius.
Therefore, the approximate size of the gravitational field on the recently discovered planet would be half of the Earth's gravitational field strength, approximately 4.9 m/s^2 (rounded to one decimal place).