Earth’s moon has an average orbital speed of 1020m/s. The average radius of the Moon’s orbit is 3.844 x 10^8m. The universal gravitational constant is approximately 6.674 x 10^-11 m^3/kgs^2. Use this data to find the mass of the Earth in kg. [Hint: Gravity is a form of centripetal force.]
We can use the equation for centripetal force to solve for the mass of the Earth. The centripetal force acting on the moon is the force of gravity between the Earth and the moon:
F = (G * m1 * m2) / r^2
where F is the centripetal force, G is the gravitational constant, m1 is the mass of the Earth, m2 is the mass of the moon, and r is the average radius of the moon's orbit.
The centripetal force can also be expressed as:
F = (m2 * v^2) / r
where v is the average orbital speed of the moon.
Setting these two equations equal to each other, we have:
(G * m1 * m2) / r^2 = (m2 * v^2) / r
Simplifying, we can cancel out the mass of the moon:
G * m1 / r^2 = v^2 / r
m1 = (v^2 * r) / (G * r^2)
Plugging in the given values:
m1 = (1020^2 * 3.844 x 10^8) / (6.674 x 10^-11 * (3.844 x 10^8)^2)
m1 = 7.351 x 10^22 kg
Therefore, the mass of the Earth is approximately 7.351 x 10^22 kg.