Given that acceleration due to gravity at the surface of the earth is 9.8N/kg, estimate a value for the mass of the earth. G=6.7x10^-11
To estimate the mass of the Earth using the given information, we can apply Newton's law of universal gravitation.
Newton's law of universal gravitation states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The formula for Newton's law of universal gravitation is:
F = (G * m1 * m2) / r^2,
where:
F is the force of gravity between two objects,
G is the gravitational constant (6.7 x 10^-11 N(m/kg)^2),
m1 and m2 are the masses of the two objects, and
r is the distance between the centers of the two objects.
In this case, one of the objects is the Earth, and the other object is a mass on the surface of the Earth. We can solve for the Earth's mass (m1) by rearranging the equation as follows:
m1 = (F * r^2) / (G * m2).
Given that the acceleration due to gravity at the surface of the Earth is 9.8 N/kg, we can use this value as the force (F). The distance between the surface of the Earth and any object on it is essentially the Earth's radius, which is approximately 6,371 km (or 6,371,000 meters).
Plugging in these values, we get:
m1 = (9.8 N/kg * (6,371,000 m)^2) / (6.7 x 10^-11 N(m/kg)^2 * m2).
Now, we need to determine the mass of an object (m2) on the surface of the Earth. For simplicity, we can assume the mass of the object is 1 kg. Therefore, we have:
m1 = (9.8 N/kg * (6,371,000 m)^2) / (6.7 x 10^-11 N(m/kg)^2 * 1 kg).
Evaluating this expression, we can estimate the mass of the Earth.