Question

Mass of the earth has been determined through
A. Use of Kepler’s $\dfrac{{{T^2}}}{{{R^3}}}$ constancy law and Moon’s period.
B. Sampling the density of earth’s crust and using earth’s radius.
C. Cavendish’s determination of $G$ and using earth radius and $g$ at its surface.
D. Use of periods of satellites at different heights above earth’s surface and known radius of earth.

Answer 1

Kepler’s constancy law explains the passage of planets around the Sun. The Cavendish experiment was the very first attempt to determine the gravitational force in the lab.

Complete step by step solution:
Kepler’s constancy law: In astronomy, Kepler's planet movement laws are three empirical rules that explain the passage of planets around the Sun. Calculations of Mars' orbit have shown the elliptical orbits of planets. From this Kepler concluded that other bodies in the Solar System may have elliptical orbits, like those further away from the Earth.

Sampling the density of earth’s crust and using earth’s radius: The distribution of density within the Earth as a function of location is much less well defined than the seismic velocities. The qualitative data derives from the Earth's mass and moment of inertia and this data alone includes mass convergence into the middle of the globe.

Cavendish’s determination of $G$ and using earth radius and $g$ at its surface: The Cavendish experiment was the very first attempt to determine the gravitational force in the lab between masses, and the very first experiment to obtain correct values for the gravitational constant. The earth's mass has been calculated by Cavendish measuring $G$ by using the radius by $g$ of earth at its surface.

Periods of satellites at different heights above earth’s surface: Geosynchronous means that every $24$ hours, the satellite will have the same time cycle as the planet, returning to the same location. The gravitational pull from the earth causes the satellite to go in orbit (otherwise it flies away. Hence gravity is the cause of the centripetal force.

Hence, option C is correct.

Note: Henry Cavendish conducted an experiment to discover the Earth's density. Other researchers utilised his experimental results to evaluate the G value. The setup consisted of a torsional equilibrium that drew lead balls together, measured the torque on a wire and then equated it with the gravitational force between the balls.