Gliese 581e is an exoplanet with a mass of 1.9 Earths that orbits a red dwarf star at a distance of 5 x1010 m (0.33 au). If its orbital period is 124 days, find the mass of the star in kg. Divide your answer by the suns mass to see how much more or less massive the star is than our sun.
+26396 Gliese 581e is an exoplanet with a mass of 1.9 Earths that orbits a red dwarf star at a distance of 5 x1010 m (0.33 au). If its orbital period is 124 days, find the mass of the star in kg. Divide your answer by the suns mass to see how much more or less massive the star is than our sun.
1au=149 597 870 700m
We have:
T=124 days=124∗24∗60∗60 s=1.07136∗107 s and
a=0.33au≈5∗1010 m and
mExoplanet=1.9∗mearthmearth=5.97219∗1024 kg see: https://en.wikipedia.org/wiki/Earth_mass
mExoplanet=1.13471610000∗1025 kg
see: https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion
T2a3=4π2G(M+m)M=4π2a3GT2−m
where
T is the orbital period of the orbiting body,
M is the mass of the star,
G is the universal gravitational constant and
a is the radius, i.e. the semi-major axis of the ellipse.
m is the mass of the orbiting body.
The gravitational constant is : see: https://en.wikipedia.org/wiki/Gravitational_constant
G=6.67384⋅10−11m3kg⋅s2
M=4π2(5∗1010 m)36.67384⋅10−11m3kg⋅s2∗(1.07136∗107 s)2−1.13471610000∗1025 kg M=4π2∗53∗10306.67384⋅10−11∗1.071362∗1014 kg−1.13471610000∗1025 kg M=4π2∗53∗1030⋅1011⋅10−146.67384∗1.071362 kg−1.13471610000∗1025 kg M=4π2∗53∗10276.67384∗1.071362 kg−1.13471610000∗1025 kg M=6.44203535336⋅1029 kg−1.13471610000∗1025 kg M=1025(6.44203535336⋅104−1.13471610000) kg M=64419.2188175⋅1025 kg Mstar=6.44192188175⋅1029 kg
Solar mass see: https://en.wikipedia.org/wiki/Solar_mass
M⊙=1.98855⋅1030 kg MstarM⊙=6.44192188175⋅1029 kg1.98855⋅1030 kg =6.44192188175⋅10−11.98855 =3.23950711913⋅10−1 =0.323950711913 Mstar=0.324 ∗M⊙
+26396 Gliese 581e is an exoplanet with a mass of 1.9 Earths that orbits a red dwarf star at a distance of 5 x1010 m (0.33 au). If its orbital period is 124 days, find the mass of the star in kg. Divide your answer by the suns mass to see how much more or less massive the star is than our sun.
1au=149 597 870 700m
We have:
T=124 days=124∗24∗60∗60 s=1.07136∗107 s and
a=0.33au≈5∗1010 m and
mExoplanet=1.9∗mearthmearth=5.97219∗1024 kg see: https://en.wikipedia.org/wiki/Earth_mass
mExoplanet=1.13471610000∗1025 kg
see: https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion
T2a3=4π2G(M+m)M=4π2a3GT2−m
where
T is the orbital period of the orbiting body,
M is the mass of the star,
G is the universal gravitational constant and
a is the radius, i.e. the semi-major axis of the ellipse.
m is the mass of the orbiting body.
The gravitational constant is : see: https://en.wikipedia.org/wiki/Gravitational_constant
G=6.67384⋅10−11m3kg⋅s2
M=4π2(5∗1010 m)36.67384⋅10−11m3kg⋅s2∗(1.07136∗107 s)2−1.13471610000∗1025 kg M=4π2∗53∗10306.67384⋅10−11∗1.071362∗1014 kg−1.13471610000∗1025 kg M=4π2∗53∗1030⋅1011⋅10−146.67384∗1.071362 kg−1.13471610000∗1025 kg M=4π2∗53∗10276.67384∗1.071362 kg−1.13471610000∗1025 kg M=6.44203535336⋅1029 kg−1.13471610000∗1025 kg M=1025(6.44203535336⋅104−1.13471610000) kg M=64419.2188175⋅1025 kg Mstar=6.44192188175⋅1029 kg
Solar mass see: https://en.wikipedia.org/wiki/Solar_mass
M⊙=1.98855⋅1030 kg MstarM⊙=6.44192188175⋅1029 kg1.98855⋅1030 kg =6.44192188175⋅10−11.98855 =3.23950711913⋅10−1 =0.323950711913 Mstar=0.324 ∗M⊙
