If the acceleration due to gravity is 9.8m/5? and
the radius of the earth is 6400km, calculate the mass of the earth,(G=6.7 × 10-11 Nm° kg-)
To calculate the mass of the Earth with the given information, we will use the formula for the acceleration due to gravity:
g = (G * M) / r^2
Where:
g = acceleration due to gravity (9.8 m/s^2)
G = gravitational constant (6.7 x 10^-11 Nm^2/kg^2)
M = mass of the Earth (unknown)
r = radius of the Earth (6400 km = 6400000 m)
Rearranging the formula, we can solve for M:
M = (g * r^2) / G
Plugging in the values:
M = (9.8 * (6400000^2)) / (6.7 x 10^-11)
Calculating this:
M = 3.0365 x 10^24 kg
Therefore, the mass of the Earth is approximately 3.0365 x 10^24 kg.
To calculate the mass of the Earth, we can use the formula:
g = (G * M) / r^2
Where:
g is the acceleration due to gravity (9.8 m/s^2)
G is the gravitational constant (6.7 × 10^-11 Nm^2/kg^2)
M is the mass of the Earth (what we want to find)
r is the radius of the Earth (6400 km or 6400000 m)
Rearranging the equation to solve for M:
M = (g * r^2) / G
Now we can substitute the values:
M = (9.8 * (6400000)^2) / (6.7 × 10^-11)
Calculating this equation will give the mass of the Earth. Let's do the math:
M = 3.03623 × 10^24 kg
Therefore, the mass of the Earth is approximately 3.03623 × 10^24 kg.