Distance from the Earth to the Sun math problem?

Question

umm I need your help! =D
I Copied this right from my math book

Distance from the Earth to the Sun:

It follows from Kepler's Third Law of planetary motion that the average distance from a planet to the sun (in meters) is:

d = ((GM/(4pi^2))^(1^3) * T^(2/3)

where M = 1.99 * 10^30 kg is the mass of the sun, G = 6.67 * 10^(-11) N * m^2/kg^2 is the gravitational constant, and T is the period of the planet's orbit(in seconds) Use the fact that the period of the earth's orbit is about 365.25 days to find the distance from the earth to the sun

I know the equations seems confusing the way I typed it out, I did the best I could but the answer I got was D = 1.4956 * 10^14

I think this is close because I looked up stuff and found the number 1.495987 * 10^11 (I dont know if this is right)

So maybe there was some kind of problem with adding/subtracting exponents? AHHH

Answer 1

The answer is right.
d = (GM/(4pi^2))^(1/3)*T^(2/3)
d = (6.67*10^(-11) * 1.99*10^30)/(4pi^2))^(1/3)
* (365.25*24*3600)^(2/3)
d = (1.32733x10^20 / (4pi^2))^(1/3)
*(31557600)^(2/3)
d = 1498096.276*99862.54841
d = 1.4960x10^11 meter

Answer 2

Did you mean to type
d = ((GM/(4pi^2))^(1/3) * T^(2/3) ?
Which would make more sense.

The numbers come out right for me. I've not included all the steps.

G is 6.67E-11
M is 1.99E+30
T is 365.25 days
So T is 31557600 secs

GM 1.33E+20
pi 3.14159
4pi^2 39.47835091

GM/(4pi^2) 3.36E+18


D= 1.49604E+11

Answer 3

T T = (365. 25 x 24 x 60 x 60) x (365. 25 x 24 x 60 x 60)
T T = 9.96 x 10 ^ (14). ~ 10 ^15

G M = 1.33 x 10 ^ (20)

G M T T = 1.33 x 10 ^ (35)

G M T T / 4 п п = 3.37 x 10 ^ (33)

(Cube)th root of this is 1.49 x 10 ^ 11 m.

Answer 4

The distance is 150 million kilometers (1.5E11 meters). So yes, the flaw is probably in exponents, or possibly in units (grams/kilograms, meters/kilometers).
Postscript: My first thougt was the same as first responder's, but that had to be discarded when I actually checked numbers.

Answer 5

93 million miles, 8 light mins