Calculating the gravity: Home: Capstone Project

Calculating the gravity

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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: $g=\frac{Gm}{r^2}$ 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: $\frac{\left(6.67e^{-11}m^3kg^{-1}s^{-2}\cdot1.99e^{30}kg\right)}{\opencurlybrace\left(147,000,000km-6378.1km\right)\cdot1000m\closecurlybrace^2}=0.00614\frac{m}{s^2}$

The bottom radius is subtracted by 6378.1km because that is the average radius of the Earth.

In the end, I got this:

$-9.8\frac{m}{s^2}_{earth}+0.00614\frac{m}{s^2}_{sun}+3.43e^{-5}\frac{m}{s^2}_{moon}+2.25e^{-7}\frac{m}{s^2}_{venus}+3.71e^{-9}\frac{m}{s^2}_{mercury}$ = $-9.7938\frac{m}{s^2}$

But the question is: Will it make a difference?

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[{:content=>"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 <a href=\"http://www.universetoday.com\">http://www.universetoday.com</a>)\nThen, I plugged them all into the equation: <img class=\"equation_image\" title=\"g=\\frac{Gm}{r^2}\" src=\"/equation_images/g%253D%255Cfrac%257BGm%257D%257Br%255E2%257D\" alt=\"g=\\frac{Gm}{r^2}\"> which would allow me to find the planet's contribution to the gravitational constant.\nSun m: 1.99e30 kg,     r: 147,000,000 km\nMercury m: 3.3e23 kg,     r: 77,000,000 km\nVenus m: 4.87e24 kg,     r: 38,000,000 km\nMoon m: 7.348e22 kg,     r: 384,4000 km\nEarth r: 6,378.1 km\n \nNow, 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.\nFg sun: <img class=\"equation_image\" title=\"\\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}\" src=\"/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\" alt=\"\\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}\">\nThe bottom radius is subtracted by 6378.1km because that is the average radius of the Earth.\nIn the end, I got this:\n<img class=\"equation_image\" title=\"-9.8\\frac{m}{s^2}_{earth}+0.00614\\frac{m}{s^2}_{sun}+3.43e^{-5}\\frac{m}{s^2}_{moon}+2.25e^{-7}\\frac{m}{s^2}_{venus}+3.71e^{-9}\\frac{m}{s^2}_{mercury}\" src=\"/equation_images/-9.8%255Cfrac%257Bm%257D%257Bs%255E2%257D_%257Bearth%257D%2B0.00614%255Cfrac%257Bm%257D%257Bs%255E2%257D_%257Bsun%257D%2B3.43e%255E%257B-5%257D%255Cfrac%257Bm%257D%257Bs%255E2%257D_%257Bmoon%257D%2B2.25e%255E%257B-7%257D%255Cfrac%257Bm%257D%257Bs%255E2%257D_%257Bvenus%257D%2B3.71e%255E%257B-9%257D%255Cfrac%257Bm%257D%257Bs%255E2%257D_%257Bmercury%257D\" alt=\"-9.8\\frac{m}{s^2}_{earth}+0.00614\\frac{m}{s^2}_{sun}+3.43e^{-5}\\frac{m}{s^2}_{moon}+2.25e^{-7}\\frac{m}{s^2}_{venus}+3.71e^{-9}\\frac{m}{s^2}_{mercury}\">= <img class=\"equation_image\" title=\"-9.7938\\frac{m}{s^2}\" src=\"/equation_images/-9.7938%255Cfrac%257Bm%257D%257Bs%255E2%257D\" alt=\"-9.7938\\frac{m}{s^2}\">\nBut the question is: Will it make a difference?", :section_type=>"rich_text"}, {:attachment_id=>24417576, :section_type=>"attachment"}]

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