What is the average distance of Mercury from the center star? Approx. 88 earth days in year on planet mercury.

Question

For each planet in the solar system, its year is the time it takes the planet to revolve around the center star. The formula E=0.2x3/2 models the number of Earth days in a planet's year, E, where X is the average distance of the planet from the center star, in millions of kilometers. There are approximately 88 Earth days in the year of the planet Mercury. What is the avergae distance of Mercury from the center star? Round to the nearest million kilometers.

Answer 1

Hi Breanna,

 

I'm assuming the formula is actually E = 0.2 X^1.5  here. This is an approximation of Kepler's Third Law.

 

If we know E (88 days), we can re-arrange the formula to get X by itself.

 

So,   88 / 0.2 = 5 * 88 = 440 = X^1.5

 

If we raise both sides to the power of 2/3, we will have X by itself and equal to 440^2/3, or X = 440^0.66666667.

 

If we look up Mercury's data, we find it has a very eccentric orbit, where the radius varies between 46 and 70 million kilometers. If we take the middle of that range, 58 million km, we find that this is pretty close to the answer we get from the equation.