The planet Neptune has gravitational field intensity of 10.3nékg at a height of 1.00*10?6m above its surface. If the radius of Neptune is 2.48*10?7m, what is its mass
To find the mass of Neptune, we can use the formula for gravitational field intensity:
g = (G * M) / r^2
where:
g is the gravitational field intensity,
G is the gravitational constant (approximately 6.67430 x 10^-11 N m^2 / kg^2),
M is the mass of the planet, and
r is the distance from the center of the planet to the point where the field is measured.
In this case, g = 10.3 N/kg and r = 1.00 x 10^-6 m. We need to solve for M.
Rearranging the formula, we can express M as:
M = (g * r^2) / G
Now, let's substitute the given values into the formula:
M = (10.3 N/kg * (1.00 x 10^-6 m)^2) / (6.67430 x 10^-11 N m^2 / kg^2)
Simplifying the equation, we get:
M = (10.3 N/kg * 1.00 x 10^-12 m^2) / (6.67430 x 10^-11 N m^2 / kg^2)
M = (10.3 N * 1.00 x 10^-12 m^2) / (6.67430 x 10^-11 N m^2)
M = 1.03 x 10^-11 N m / (6.67430 x 10^-11)
M = 0.1544 kg
Therefore, the mass of Neptune is approximately 0.1544 kg