- Sirius_Alpha wrote:
- The mass of the star is quoted as 1.00 ± 0.22 Msol But the planet mass has a much lower error, 0.64 ± 0.09 MJ. Why is the planet's mass much more constrained than the stars?
Good question.
From the equations of motion it is possible to write the expressions for star and planet mass as follows:
m
1 = (P K
23 (1 + K
1 / K
2)
2) / (2π G sin
3 i)
swap index 1 and 2 to get planet mass.
Error bars are given for K
1, K
2 and i, so the error on the mass can be expressed:
σ
m2 = ((∂m / ∂K
1) σ
K₁)
2 + ((∂m / ∂K
2) σ
K₂)
2 + ((∂m / ∂i) σ
i)
2Working through that does give the uncertainties quoted in the paper, so that all checks out.
Uncertainty basically comes down to which of K
23(1 + K
1/K
2)
2 (in the expression for star mass) and K
13(1 + K
2/K
1)
2 (in the expression for planet mass) has greater uncertainty.
Very handwavey way of looking at it, K
2 has significantly higher uncertainty than K
1, and in the expression for star mass the highest order term is in K
23 as opposed to K
22 in the expression for planet mass.