A white dwarf in a binary system has a radius of 7000 km and a mass equal (minus an infinitesimal amount) to the Chandrasekhar limit of 1.4M sun. The companion transfers an infinitesimal amount of mass to the white dwarf which is enough to send it over the Chandrasekhar limit and it collapses to a neutron star with a radius of 14 km. Calculate the amount of gravitational potential energy released. NOTE: we can assume that the mass of the neutron star once is triggered and the mass of the WD are both equal to the Chandrasekhar mass in this case.

A child in a boat throws a 5.7kg package out horiontally with a speed of 10.0m/s. Calculate the velocity of the boat immediately after, assuming it was intially at rest. The mass of the child is 24.0kg and that of the boat is 35.0kg.

38 An AGN hosts a central Black Hole of mass ×ばつ10 kg. The AGN emits at 1/6 of the Eddington limit. Find the luminosity of the AGN. Give your answer in Watts to 3 significant figures.

Let's compare the acceleration due to gravity at the surface of a Sun-like star to a white dwarf of similar mass. We know that the force of gravity comes from F= G*m_1*m_2/r^2 and that F = m * a from some of Newton's laws. As such, we know that the acceleration due to gravity is given by a_g = G*m/r^2. With that in mind, let's say that we have a white dwarf star is approximately the size of the Earth which is 1/100 radius of the Sun (0.01 R Sun) and that the white dwarf has a mass that is approximately half the mass of the Sun (0.5 M_Sun). What is the ratio of the acceleration due to gravity at the surface of the white dwarf star (aka the surface gravity) compared to the surface gravity of the Sun-like star (assume its mass is 1 M_sun and radius is 1 R_Sun).?

A Type la supernova is observed and achieves an apparent magnitude of m = 19.89 at peak brightness. The absolute magnitudes of Type la supernovae at peak brightness are known to be M = –19. Determine the distance to the supernovae in units of Мрс. Select one: а. 600 O b. 1000 О с 10 O d. 200 е. 300

Calculate the redshift caused by a neutron star with a radius of 11 km and mass of 5.2 x 1030 kg.

After the Sun exhausts its nuclear fuel, its ultimate fate may be to collapse to a white dwarf state. In this state, it would have approximately the same mass as it has now, but its radius would be equal to the radius of the Earth.Calculate the average density of the white dwarf.Calculate the surface free-fall acceleration.Calculate the gravitational potential energy associated with a 6.69-kg object at the surface of the white dwarf.

International Astronomical Union reported on 24 Feb 1987: An object was discovered on Feb. 24.37 UT (position R.A. = 5h35m.8, Decl. = -69 18'), obtained m = 4.8 on Feb. 24.454 UT. This object proved to be the most famous supernova (SN) in the 20th Century and the brightest visible from Earth since 1604. It is classified as a SN of the type Il in the Large Magellanic Cloud (SN1987A). Its brightness peaked in May 1987, with an apparent magnitude of m = 2.8. a) Find the absolute magnitude M of the SN1987A at maximum. Distance of the LMC is 51,400 pc. b) The progenitor (before SN explosion) star was a blue supergiant of the apparent magnitude m = 12.8. How much brighter (in terms of flux density) this SN was at maximum compared to the progenitor star. Find the ratio FSN / Ebefore

The typical core-collapse supernova has an energy budget of about 1046 J. This energy comes from the gravitational potential energy of an inner core with mass Mic, which collapses from an initial radius of 5 x 106 m down to the final radius of 50 km. Estimate Mic, in solar masses, for this to be a realistic energy source of the core-collapse supernova. You may assume that the density before the collapse is uniform. Discuss briefly how a Type la supernova is different from a core-collapse supernova from a massive star?

Assume a neutron star has a mass of about 1.2 times the mass of the Sun and a radius of 7 kilometers. If the escape speed is V2esc=2GM/R, work out the formula for the radius of the Event Horizon around a Black Hole of mass M.

= 2000 K and a radius of R, A young recently formed planet has a surface temperature T Jupiter radii (where Jupiter's radius is 7 x 107 m). Calculate the luminosity of the planet and 2 determine the ratio of the planet's luminosity to that of the Sun.

True or false The escape speed from a black hole would be greater than the speed of light. If the impact time of a collision is increased, the force of impact will decrease. A size of a Kelvin degree (oK) is larger than a Celsius degree (oC).

A main sequence star of mass 25 M⊙has a luminosity of approximately 80,000 L⊙. a. At what rate DOES MASS VANISH as H is fused to He in the star’s core? Note: When we say "mass vanish '' what we really mean is "gets converted into energy and leaves the star as light". Note: approximate answer: 3.55 E14 kg/s b. At what rate is H converted into He? To do this you need to take into account that for every kg of hydrogen burned, only 0.7% gets converted into energy while the rest turns into helium. Approximate answer = 5E16 kg/s c. Assuming that only the 10% of the star’s mass in the central regions will get hot enough for fusion, calculate the main sequence lifetime of the star. Put your answer in years, and compare it to the lifetime of the Sun. It should be much, much shorter. Approximate answer: 30 million years.