Calculate the orbital distance (semi-major axis) for an extra-solar planet in a 3.312 Earth-day orbit around a 1.3 solar-mass star.?

Select one:
a. 0.068 AU
b. 0.058 AU
c. 0.038 AU
d. 0.048 AU
e. 0.078 AU

Select one:
a. 0.068 AU
b. 0.058 AU
c. 0.038 AU
d. 0.048 AU
e. 0.078 AU

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May 27, 2017

Answer:

The semi-major axis is 0.048AU, answer d.

Explanation:

The orbital period #p# in years and the semi-major axis #a# in AU of an orbiting body are related by Newton's form of Kepler's third law.

#Mp^2=a^3#

Where #M# is the mass of the star in solar masses.

Substituting the values and converting days to years gives:

#a^3=1.3*3.312^2/365^2=0.000107#

Taking the cube root gives #a=0.04748#.

So the nearest answer is d. 0.048AU.

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