You are observing an exoplanet (a planet orbiting a star other than our Sun). Like many of the earliest exoplanets that were discovered, the planet is a "hot Jupiter", a gas giant that orbits its star closer than Earth orbits our Sun. You can assume the mass of the planet is much smaller than the mass of the star and can be neglected. If the mass of the star is 0.54 solar masses, and the period of the orbit is 6.06 days, what is the distance from the star to the planet in AU? 1 AU E
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- The rate at which a nebular cloud rotates increases as the cloud collapses to form systems of stars and planets. Consider a small segment of a nebular cloud with a mass m of 1.9 x 102" kg, tangential velocity vinitial equal to 6.8 km s-1 located at an orbital distance rinitial = 2.5 x 10* km. After the cloud collapses, the same small segment is located at an orbital distance rinal = 3.2 x 10° km. Calculate the change of the rotational velocity, Ao, for the cloud segment, assuming perfectly circular orbits. Perform your work and report your solution using two significant figures. Δω- 16605 rad s-!Consider a star of mass M₁ that hosts a planet of mass M₂ on a circular orbit with semi- major axis a. The mass of the planet is related to the orbital velocity of the star by the expression G M₂1 Μια Using Kepler's 3rd law show that this expression can be written as V₁ = 2πG (27²) ¹/3 9 M²P where P is the orbital period of the planet around the star. V₁ = M₂The star HD 69830's mass is 1.7 ✕ 1030 kg, its radius is 6.3 ✕ 105 km, and it has a rotational period of approximately 35 days. If HD 69830 should collapse into a white dwarf of radius 7.8 ✕ 103 km, what would its period (in s) be if no mass were ejected and a sphere of uniform density can model HD 69830 both before and after?
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- What is the escape velocity is km/s from Jupiters exosphere, which begins about 993 km above the surface ? Assume the Gravitational constant is G= 6.67 x10-11m3 kg-1s-2, and that's Jupiter has a mass of 1.8999999999999998e+27kg and a radius of 68.0 x103kmNeptune has a mass of 1.0 × 1026 kg and is 4.5 × 109 km from the Sun with an orbital period of 165 years. Planetesimals in the outer primordial solar system 4.5 billion years ago coalesced into Neptune over hundreds of millions of years. If the primordial disk that evolved into our present day solar system had a radius of 1011 km and if the matter that made up these planetesimals that later became Neptune was spread out evenly on the edges of it, what was the orbital period of the outer edges of the primordial disk?