A mass of 1kg on the earth is attracted with a force of 9,8 N.The raduis ofthe earth is 6,38 X 10m,calculate the mass of the earth.
To calculate the mass of the Earth, we can use Newton's law of universal gravitation, which states that the gravitational force between two objects is given by the equation:
F = G * (m₁ * m₂) / r²
Where:
F is the gravitational force
G is the gravitational constant (approximately 6.67430 × 10^-11 N(m/kg)²)
m₁ and m₂ are the masses of the two objects
r is the distance between the centers of the two objects
In this case, we know the gravitational force (F) acting between a mass of 1 kg and the Earth is 9.8 N, and the radius (r) of the Earth is 6.38 × 10^6 m.
Plugging these values into the equation, we get:
9.8 N = G * (m₁ * m₂) / (6.38 × 10^6 m)²
Now, since we are finding the mass of the Earth (m₂), we can assume that the mass of the object (m₁) is negligibly small compared to the mass of the Earth. Therefore, we can rewrite the equation as:
9.8 N = G * (m₁ * m₂) / (radius of the Earth)²
Simplifying further, we get:
m₂ = (9.8 N * (radius of the Earth)²) / G
Now, substituting the known values:
m₂ = (9.8 N * (6.38 × 10^6 m)²) / (6.67430 × 10^-11 N(m/kg)²)
Calculating this expression will give you the mass of the Earth.
Note: The value of gravitational constant G used in this equation is an accepted average value. The exact value of G is known to have some variation in very precise measurements.