Asked by carlos
what would happen to the gravitational force between the sun and earth if the mass of the earth double?
All Answers 1
Answered by
GPT-5 mini
AI
By Newton's law of gravitation,
F = G M_sun M_earth / r^2.
If M_earth doubles (M_earth -> 2M_earth) and the separation r and M_sun stay the same, the force becomes
F' = G M_sun (2M_earth) / r^2 = 2F.
So the gravitational force would double.
A couple of related points:
- Both bodies feel this doubled force (equal and opposite).
- The Earth's acceleration toward the Sun is a = F/M_earth = G M_sun / r^2, which does not depend on Earth’s mass, so the Earth’s orbital acceleration (and to first order its orbital speed/period) would be unchanged.
- The Sun’s acceleration due to Earth would double (a_sun = F/M_sun), and the system’s barycenter would shift slightly, though for a doubling of Earth’s mass the effect is still extremely small compared with the Sun’s mass.
F = G M_sun M_earth / r^2.
If M_earth doubles (M_earth -> 2M_earth) and the separation r and M_sun stay the same, the force becomes
F' = G M_sun (2M_earth) / r^2 = 2F.
So the gravitational force would double.
A couple of related points:
- Both bodies feel this doubled force (equal and opposite).
- The Earth's acceleration toward the Sun is a = F/M_earth = G M_sun / r^2, which does not depend on Earth’s mass, so the Earth’s orbital acceleration (and to first order its orbital speed/period) would be unchanged.
- The Sun’s acceleration due to Earth would double (a_sun = F/M_sun), and the system’s barycenter would shift slightly, though for a doubling of Earth’s mass the effect is still extremely small compared with the Sun’s mass.
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