- #1
Omnistegan
- 3
- 0
Homework Statement
One stellar mass is defined as the mass of our sun (1Ms = 1.99 x 1030 kg). ONe astronomical unit is defined as the length of Earth's semi-major axis (1AU = 1.49 x 1011 m). The star Epsilon Eridani in the constellation Eridanus has a planet (discovered in 2000) orbiting it that has a semi-major axis of 3.39 AU. The orbital period of the planet is 6.54 years. Based on this information, determine the mass of Epsilon Eridani in stellar masses (Ms).
Homework Equations
[tex]F_{c} = F_{g}[/tex]
[tex]F_{c} = \frac{4\pi^2r}{T^2}[/tex]
[tex]F_{g} = \frac{Gm_{1}m_{2}}{r^2}[/tex]
The Attempt at a Solution
mp is the mass of the planet, me is the mass of Epsilon Eridani
[tex]\frac{4\pi^2m_{p}r}{T^2} = \frac{Gm_{p}m_{e}}{r^2}[/tex]
Solve for me, the mp's cancel
[tex]m_{e} = \frac{4\pi^2r^3}{T^2G} = \frac{4\pi^2\left(3.39 \times 1.49\times 10^{11}\right)^3}{\left(6.54 \times 365 \times 24 \times 3600\right)\left(6.67\times 10^{-11}\right)} = 1.79 \times 10^{30}[/tex]
now divide that answer by kg in a Stellar Mass
[tex]\frac{1.79 \times 10^{30}}{1.99 \times 10^{30}} = 0.901M_{s}[/tex]
Apparently the correct answer is 0.903Ms. I did have a chance to clarify with my teacher that 365x24x3600 is what he expected us to use for seconds.
Any help is appreciated!