If the distance from the centre of the Earth to the centre of the Sun was kept constant and the mass of the Earth was halved, what would happen to the force of gravity?
Would the force of gravity acting on both the Sun and Earth double in magnitude? I'm kind of confused...
To understand what would happen to the force of gravity if the mass of the Earth was halved while keeping the distance between the Earth and the Sun constant, we can use Newton's law of universal gravitation. This law 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.
So, let's break it down step by step to clarify it:
1. Newton's law of universal gravitation equation:
F = G * (m1 * m2) / r^2
F represents the force of gravity between the Earth and the Sun.
G is the gravitational constant.
m1 and m2 are the masses of the Earth and the Sun, respectively.
r is the distance between the centers of the Earth and the Sun.
2. If the distance between the Earth and the Sun remains constant, it means that 'r' would not change in this scenario.
3. If we halve the mass of the Earth, let's call it 'm1_new', the modified equation becomes:
F_new = G * (m1_new * m2) / r^2
4. Since the mass of the Earth is halved, we can express 'm1_new' as (m1 / 2):
F_new = G * ((m1 / 2) * m2) / r^2
5. Simplifying the equation:
F_new = (G * m1 * m2) / (2 * r^2)
Comparing the modified force of gravity, F_new, to the original force of gravity, F, we can see that F_new is half of F. Thus, if the mass of the Earth is halved while keeping the distance constant, the force of gravity between the Earth and the Sun would decrease by half. This implies that the force of gravity acting on both the Sun and the Earth would be reduced by half in magnitude.
In summary, halving the mass of the Earth would result in a proportional decrease in the force of gravity between the Earth and the Sun.