The relation between the # of time in days, D, it takes for a planet to revolve around the Sun is related to the planer's average distance from the Sun, k, in millions of kilometres is defined by log D= 3/2logk-0.7 .
How much longer does it take Mars than
Venus to orbit the Sun if Mars is 207 million km and Venus is 108 million km away from the Sun?
The answer i got was originally 0.424.. but it seemed off to be so i tried it a different way and got 2.3 , can someone tell me which is correct?
you will have to use brackets so I can tell what the order of operation is
The way you typed it it would be
D = (3/2)logk - 0.7
but I have a feeling it could be
D = 3/(2logk) - .07 or even
D = 3/(2logk - 0.7)
opps, im sorry.. its suppose to be D = (3/2)logk - 0.7
so for Mars k = 207 and
D = (3/2)log207 - .07 = 2.774
for Venus k = 108 and
D = (3/2)log108 - .7 = 2.350
the difference between these two times is .4238 days, which matches appr. your first answer.
To determine how much longer it takes Mars than Venus to orbit the Sun, we need to substitute the average distances for Mars and Venus into the given equation and compare the resulting values for D.
Let's start by substituting the values into the equation:
For Mars:
log(D) = (3/2)log(k) - 0.7
log(D) = (3/2)log(207) - 0.7
For Venus:
log(D) = (3/2)log(k) - 0.7
log(D) = (3/2)log(108) - 0.7
To simplify the calculations, we can raise both sides of the equation to base 10, which allows us to eliminate the logarithm:
For Mars:
D = 10^((3/2)log(207) - 0.7)
For Venus:
D = 10^((3/2)log(108) - 0.7)
Now, let's plug these equations into a calculator or spreadsheet to find the values for D:
For Mars, using the given equation and substituting the values:
D = 10^((3/2)log(207) - 0.7)
D ≈ 3.092
For Venus, using the given equation and substituting the values:
D = 10^((3/2)log(108) - 0.7)
D ≈ 0.772
To find the difference in orbit times, we can take the ratio of the orbit times:
Difference = (Time for Mars - Time for Venus)/ Time for Venus
Difference ≈ (3.092 - 0.772)/0.772
Calculating the value:
Difference ≈ 2.320
Therefore, the correct answer is approximately 2.320.