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OCR Cosmology January 2004 Question

How do you work out Question 1b on January 2004, I've looked at the markscheme, but can't work out the answer, how do I do the Maths, to work out the distance, thanks.

http://pastpapers.org/AS/physics/cosmology/Cos_04_Jan_MS.pdf

http://pastpapers.org/AS/physics/cosmology/Cos_04_Jan.pdf

Reply 1

hoppin along

Kepler's third law says that the period of the orbit squared is proportional to the distance cubed.

T^2 = k d^3

Work out the value for k from the data given about Triton then you can find the distance for Proteus.

Reply 2

QE5

But how do you put the numbers in the calculator?, I've seen the mark scheme but cant do it.?

Reply 3

hoppin along

For Triton:
d = 3.55 x 10^5
T = 5.88
k = T^2 / d^3 = (5.88)^2 / (3.55 x 10^5)^3 = 7.73 x 10^-16

Then for Proteus
T = 1.12
d^3 = T^2 / k = (1.12)^2 / 7.73 x 10^-16 = 1.64 x 10^15
d = 1.18 x 10^5