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How far does an object fall in the first 12.0 seconds when dropped from an airplane?

A sun-like star is torn apart by the tidal force (differential attraction) of a black hole of mass 1 million solar masses. It forms an accretion disk around a black hole which quickly flows into a black hole releasing 1/4 of its rest mass in the form of radiation during a time equal to one orbital period at the radius of the black hole horizon (Schwarzschild radius). What power in watts and in units of solar luminosity is emitted and for how long? Would a less massive black hole produce a smaller or larger luminosity? Is the released energy larger or smaller than the energy obtainable from the star via hydrogen fusion?

Galaxy NGC2300 has an flat disk dominating the visible light image. Surface brightness is given by

the exponential law

I(R) = I0 exp(−R/Rd)

where I0 is the central surface brightness, R distance from the center, and Rd = 4 kpc the exponential

radial scale of the disk (e-folding distance). The total luminosity of the galaxy equals L = (2.5·10^10)L(sun).

Considering that the total luminosity is surface brightness I(R) integrated over the area of the

whole disk from R = 0 to R = ∞ (not over the radial distance, a mistake some people make!), compute

I0 (in units of L(sun)/pc^2)

the exponential law

I(R) = I0 exp(−R/Rd)

where I0 is the central surface brightness, R distance from the center, and Rd = 4 kpc the exponential

radial scale of the disk (e-folding distance). The total luminosity of the galaxy equals L = (2.5·10^10)L(sun).

Considering that the total luminosity is surface brightness I(R) integrated over the area of the

whole disk from R = 0 to R = ∞ (not over the radial distance, a mistake some people make!), compute

I0 (in units of L(sun)/pc^2)

I learned Kepler's second law which was about equal areas and we PROVED that law of areas mathematically and also in his third law we PROVED, mathematically, that the period squared is equal to semi-major axis cubed, but in his first law which is:"All planets move about the Sun in elliptical orbits, having the Sun as one of the foci" we did not PROVE this law. My instructor just said that "as L is constant, which implies that the orbit lies in a plane!" It just says that the orbit lies in a plane, not that it is elliptical which is actually the law. Should not we be proving that the orbit is elliptical with Sun as on of the foci? Or am I missing something?

An astronomical object has its mass 4 times the mass of earth and radius half of the radius of

earth. If acceleration due to gravity at earth is g, find its value at the surface of the astronomical

object.

earth. If acceleration due to gravity at earth is g, find its value at the surface of the astronomical

object.

an acceleration force of 500N changes an object from 40m/sec to 60m/sec in a distance of 100m. the mass is 25 kg. determine the force of friction acting opposite this force

what formula should I use to answer a question such as the one below when my normal formula doesn't fit:

'The radius of the Earth is 6400km, the height of a geostationary satellite is 35000km above the earth's surface. What is the speed of the geostationary satellite?'

'The radius of the Earth is 6400km, the height of a geostationary satellite is 35000km above the earth's surface. What is the speed of the geostationary satellite?'

If the temperature of the background radiation today is 3 K, at what time after the

birth of the universe was the temperature 10^15 K. Take the age of the universe as

15 × 10^9 years.

birth of the universe was the temperature 10^15 K. Take the age of the universe as

15 × 10^9 years.

Ques. What is cosmic background radiation? Explain why it is so important to the debate

between evolving and a steady-state universe.

between evolving and a steady-state universe.

With the help of a diagram, explain the unified scheme for understanding active

galactic nuclei.

galactic nuclei.