Question

Before leaving Alpha Centauri, you change from the shuttle to a light speed interstellar cruiser and head out deep into the galaxy to visit another binary star system - but this one is composed of dead stars! To occupy your waking travel time by reading about this star system in the "Outer Space Tourbook": Stars spend most of their lifetimes undergoing nuclear fusion in their cores, which is why they give off so much light. However, when the material necessary for fusion is depleted, the stars are said to die, as they can no longer output very much energy. In cases of the largest and most massive stars (about 3% o all stars , stellar deaths are accompa exotic stellar remnants, including Neutron Stars and Black Holes nied by a supernova explosion and leave behind you read further, you find that the star system you are approaching is composed of two stellar remnants orbiting their common center of mass: A Neutron Star and a Black Hole. You're not quite sure what a Neutron Star is, so you read the Tourbook's description Neutron stars are much more dense than typical materials found on the surface of the Earth Typical neutron stars have a radius ofonly 12 km (slightly larger than the city of Livermore, which is 8km across), but are twice as massive as the Sun." What! Something the mass of the Sun compressed into the size of a city? You run the numbers and calculate the density of a neutron star. Show your work below. Dr. Robin Rehagen (slightly modified by E.Harpell)/ LPC Physics To compare this value for the density of a Neutron star to the densities of other familiar objects, take the ratio of the s/ for the following substances: iron, water (found in the Europa problem above), and an atomic nucleus (3* 1014 g/cm3). It's often said that "matter is made up of mostly empty space". What does this phrase mean? Does this phrase apply to a Neutron Star? Why or why not? What is your weight on the Neutron Star? You may use your results from the second problem in the lab. Show work below. weightontheNe tron Star lbs) Weight on the Neutron Star (lbs.) weight on Earth (lbs) 3a IS

Answer 1

I am using the information given in first image

R = 12 km

m = 2 times mass of sun

so,

volume of neutron star = 4/3 * pi * (12000)³ = 7.238e12

therefore,

density = mass / volume

density = 2 * 1.9891e30 / 7.238e12

density = 5.5e17 Kg/m³

Now, let's compare

with water, 5.5e17 / 1000 = 5.5e14

with iron, 5.5e17 / 7870 = 6.98e13

with atomic nucleus, 5.5e17 / 3e17 = 1.833

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To find weight on any other celestial body, we need to know value of 'g'

so,

g = GM / r²

g = 6.67e-11 * 2 * 1.9891e30 / 12000²

g = 1.85e12 m/s²

so,

weight on neutron star = mass on earth * g

( I have a doubt here, the table at last says weight on earth but units given as lbs which is usually mass, so is it weight or mass ???? please be clear)