Question

During ancient times, people believed that the Earth was the centre of the universe and all celestial bodies including the Sun revolved around the Earth. If this hypothesis were to be true, then

• A. Earth's mass should be proportionally much higher than the mass of Sun
• B. Sun's mass should be proportionally much higher than the mass of Earth
• C. Mass of Earth and Sun should be comparable
• D. The sum of masses of all celestial bodies should be comparable to that of the Earth

Answer 1

The correct option is A Earth's mass should be proportionally much higher than the mass of Sun

Consider that the hypothesis is true and the Sun revolves around the Earth. We know that for any two bodies, the gravitational force exerted by one body over the other is equal to the force exerted by the second body on the first. However, the acceleration due to gravity is inversely proportional to their masses, because
Gravitational force $F=mg\Rightarrow g=\frac{F}{m}$
Hence, the given hypothesis could only be true if the mass of Earth is much larger than that of the Sun since for the Sun to revolve around the Earth, it should have a much larger acceleration than that of the Earth.