A Brief Question about the Universal constant G

[Curious123]

1. This only relates to a homework assignment, my curiosity lies in the effects of increasing the magnitude of G. Would this affect the Earth's orbiting of the sun? I assume that individuals an objects would experience gravity differently but I do not understand how specifically. Would their actual mass increase? Any information about basic effects would be appreciated. Thank you.



2. G=(6.67428+-0.00067)x10^-11m^3kg^-1s^-2
F=G(m1xm2/r^2)

The Attempt at a Solution

 

[Delphi51]

Welcome to PF, Curious.
Interesting question! If G grew larger, then the force of the sun on the Earth would increase according to the formula F = GMm/d². The Earth's speed would no longer be sufficient to maintain a circular orbit. It would be pulled closer to the sun as it goes around, and would form an elliptical orbit with perigee closer to the sun.

The same argument applies to persons on the surface of the Earth. The same formula shows an increased force of gravity even though the mass of the Earth and the mass of the person remains the same.

I think the idea of increasing G has been toyed with before, but there is a big difficulty with it. As G gets bigger, the gravitational potential energy of all objects under the influence of gravity increases. We are pretty sure energy is conserved, so any theory that indicates increasing energy is probably wrong.

 

[Curious123]

thanks