In order to find the amount the planets change the gravitational constant,I needed to find the values of m, which is the mass of the planet/sun, and r, which is the distance from the Earth to the planet/sun. Because the planets orbit in an elliptical shape and the distance from earth can vary extremely, I used the lowest known value for r for each individual planet (and the sun. Fun fact: the point where the earth is closest to the sun is called it's Parihelion). (These m and lowest r values are according to http://www.universetoday.com)
Then, I plugged them all into the equation:
which would allow me to find the planet's contribution to the gravitational constant.
Sun m: 1.99e30 kg, r: 147,000,000 km
Mercury m: 3.3e23 kg, r: 77,000,000 km
Venus m: 4.87e24 kg, r: 38,000,000 km
Moon m: 7.348e22 kg, r: 384,4000 km
Earth r: 6,378.1 km
Now, I shall spare you all the horror of looking at all those calculations, because, trust me, it isn't pretty. I'll give you an example, though.
Fg sun: ![\frac{\left(6.67e^{-11}m^3kg^{-1}s^{-2}\cdot1.99e^{30}kg\right)}{\opencurlybrace\left(147,000,000km-6378.1km\right)\cdot1000m\closecurlybrace^2}=0.00614\frac{m}{s^2} \frac{\left(6.67e^{-11}m^3kg^{-1}s^{-2}\cdot1.99e^{30}kg\right)}{\opencurlybrace\left(147,000,000km-6378.1km\right)\cdot1000m\closecurlybrace^2}=0.00614\frac{m}{s^2}](/equation_images/%255Cfrac%257B%255Cleft%25286.67e%255E%257B-11%257Dm%255E3kg%255E%257B-1%257Ds%255E%257B-2%257D%255Ccdot1.99e%255E%257B30%257Dkg%255Cright%2529%257D%257B%255Copencurlybrace%255Cleft%2528147%252C000%252C000km-6378.1km%255Cright%2529%255Ccdot1000m%255Cclosecurlybrace%255E2%257D%253D0.00614%255Cfrac%257Bm%257D%257Bs%255E2%257D)
The bottom radius is subtracted by 6378.1km because that is the average radius of the Earth.
In the end, I got this:
= ![-9.7938\frac{m}{s^2} -9.7938\frac{m}{s^2}](/equation_images/-9.7938%255Cfrac%257Bm%257D%257Bs%255E2%257D)
But the question is: Will it make a difference?