Black Hole Gravity II. If a person was falling feet first into a 10-solar-mass black hole and his feet were at the Schwarzschild radius, what is the gravitational acceleration at his head? Assume the person is 2 m tall. Express your answer in units of m/s2. Assume gravitational acceleration is g=GM/r^2

B4

T2 6.) On planet LV-426, it is observed that a person's weight is the same as it is on Earth, but the planet has a radius half that of Earth. Which of the following must be true? Explain your answer. a.) The mass of LV-426 is 1/4 that of Earth. b.) The mass of Earth is 1/4 that of LV-426. c.) A rock dropped from 10m would hit the ground faster on Earth. d.) A rock dropped from10mwould hit the ground faster on LV-426.

Which of these would be a good frame of reference for describing motion using Newton's methods? Pick all that apply.     What Newton termed an "inertial frame of reference", meaning in effect a frame that is not accelerating.     All the universe. That is, an average of everything around us that is not part of the system we are studying.       Any frame. It doesn't matter.     The rotating Earth.

Two newly discovered planets follow circular orbits around a star in a distant part of the galaxy. The orbital speeds of the planets are determined to be 35.1km/s and 53.1km/s. The slower planet's orbital speed is 7.53years. What is the mass of the star, and what is the orbital period of the faster planet, in years?

What is the mass (in kg) of the Z0 ? What is the ratio of the mass of the Z0 to the mass of the proton?

2. Integrate the equations of motion for a spherical pendulum, i.e., a particle of mass m moving on the surface of a sphere of radius / in a gravitational field, with Lagrangian L = ml² -(0² + psin² 0) + mglcos 0. 2 Hint: Merely set up the integrals, do not evaluate them. You should obtain two integrals w.r.t. de: one determining t and another determining p. Express the first integral in terms of E,Ueff, m, and l. Express the second integral in terms of E,U eff, m, l, and M₂.

Considering both special relativity and gravity, how much does Alice age if Julie ages 1 year?

Black holes are difficult to observewith telescopes because they, bydefinition, don’t emit or reflect any light. They can be found by look-ing for other nearby objects orbit-ing them, however. Here is a dia-gram of a star in a circular orbit around a black hole. a. The period of the star’s orbit is 90 days, and its orbital radius around the black hole isobserved to be 3.6 : ×10^11 m. Find the orbital velocity of the star in units of m/s. (You need to convert 90 days to seconds, first). The circumference of a circle is 2πr.  b. The mass of the star is known to be 4 × 10^30 kg. Find the centripetal acceleration of thestar and the strength of the gravitational force on the star.  c. Find the mass of the black hole.

3) The new Earth-Pluto SuperShuttle boasts that it can take you between the two planets, which are 5.0 hours apart in 2.5 hours (according to your watch). What time interval is measured by people in the Earth-Pluto frame? What is the shuttle's speed?