Using the fact that a 1.0 kg mass weighs 9.8N on the surface of the earth and the radius of the earth is roughly 6.4x10^8m.
calculate the mass of the earth.
Use the weight and mass m to get g = 9.8 m/s^2. Then use
g = G m M/R^2 to get the earth's mass M.
G is the universal gravity constant of Newton. Look it up.
To calculate the mass of the earth using the given information, we can apply Newton's law of universal gravitation.
The equation is:
F = G * (m1 * m2) / r^2
where:
F = force of gravity
G = gravitational constant (approximately 6.67430 × 10^-11 N m^2/kg^2)
m1 = mass of one object
m2 = mass of the other object
r = distance between the centers of the two objects
In this case, we can assume that the mass of the 1.0 kg object is m1 and the mass of the earth is m2.
Given:
F = 9.8 N
m1 = 1.0 kg
r = 6.4 × 10^8 m
We need to solve the equation for m2, the mass of the earth.
First, rearrange the equation to solve for m2:
m2 = (F * r^2) / (G * m1)
Now, substitute the given values into the equation:
m2 = (9.8 N * (6.4 × 10^8 m)^2) / (6.67430 × 10^-11 N m^2/kg^2 * 1.0 kg)
Calculating this expression will give us the mass of the earth.