A spaceship is located around 2.6×10¹³ km from the black hole Messier 87. It has a mass of 6.6 billion suns. How long will their day last compared to a day on Earth?
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- Time is not absolute, it depends on the speed and gravitational field present. The time measured will be slower when there is a large gravitational field present.
- When the clock is closer to the gravitational source slower the time measured. This effect is called gravitational time dilation.
- Gravitational time dilation is given by,
Here t is the change in time in the gravitationally influenced reference frame, t0 is the change in time in a reference frame an infinite distance from any mass (a "standard" hour), c is the speed of light, G is the gravitational constant, M is the mass of the object being approached, and r the distance from the object being approached
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- A non-rotating black hole has an ‘edge’ at what’s called it’s Schwartzschildradius. For a black hole of mass M, the Schwartzschild radius isRSch = 2GM/(c^2) where G is the gravitational constant and c is the speed of light. Close to black holes, we really should use Einstein’s theory of gravity (General Relativity) instead of Newton’s, but Newton’s is still a good approximation.Using Newtonian Gravity, find the gravitational force on a mass m at theSchwartzschild radius of a black hole. (Your answer for this should look likeFgrav = an expression in terms of G, M, m, c and numbers.) Is the forcesmaller or larger for a more massive black hole?The acceleration of gravity near a black hole is so large that not even light can escape. Which two factors would increase the acceleration of gravity near a black hole? O A black hole with more mass and the same radius A black hole with a larger radius and the same mass A black hole with less mass and the same radius A black hole with a smaller radius and the same mass O O OThe pilot of a space ship shines a laser pointer from the back of the ship to the front. The laser travels at the speed of light 300,000 km/s with respect to the ship, which is itself moving at 100,000 km/s. What will be the speed of the laser beam according to an observer at rest outside the ship? Express your answer in km/s
- The mass of an electron is 9.11 x 10 ^-31 kg. The mass of a proton is 1.67 x 10 ^-27 kg. They are about 5.3×10^ −11 m apart in a hydrogen atom. What is the gravitational force between these two particles in the hydrogenatom?The Oort Cloud extends out to (possibly) one light-year from the sun. Objects in the Oort Cloud are still gravitationally bound to the sun. Suppose one such iceball orbits the sun in a circle. I'm going to alter some numbers, such as the mass of the sun and even G. The gravitational force is directed toward the sun and has the following magnitude: Calculate the force on the object if these are the numbers: G = 6.1*10-11 N*m2/kg2 M = 2.7*1030 kg m = 1.5*108 kg r = 19*1015 m Calculate your answer in microNewtons (10-6 N).A black hole has a schwarzschild radius of 25 km. How much mass is contained in the black hole?
- A space probe of mass 3.9 x 103 kg is orbiting a star of mass 3.6 x 1030 kg in a circular orbit at a distance of 1.7 x 1011 m from its center. Calculate the minimum energy, in units of 109 J, required to transfer the probe to a circular orbit 5.5 x 1011 m from the star. Use G = 6.7 x 10-11 N m2/ kg2. (Please answer to the fourth decimal place - i.e 14.3225)In 1999, scientists discovered a new class of black holes with masses 100 to 10,000 times the mass of our sun that occupy less space than our moon. Suppose that one of these black holes has a mass of 1x10^3 suns and a radius equal to one-half the radius of our moon. What is the density of the black hole in g/cm^3? The radius of our sun is 7.0x10^5 km, and it has an average density of 1.4x10^3 kg/m^3. The diameter of the moon is 2.16x10^3 miles.The energy to mové a rocket (mass m) nfinitely far from the Earth (Radius R and mass M) E = jGMma 1 E = x? 2 is What escape velocity at liftoff gives an energy that equals E. R
- The Millennium Falcon is approximately 35.2 m long. There are conflicting reports, but the Fàlcon made the Kessel Run in approximately 12.95 parsecs. This is an odd unit to measure speed with as a parsec is a unit of length equal to 3.26 light-year. The science FICTION comes in when you consider that ships in Star Wars use hyperdrive to travel faster than the speed of light, so they are able to make jumps through space. Han Solo picked difficult or dangerous points to jump between to make the trip so short.tet's imagine that the Millennium Falcon travels at 0.95c during the 12.95 parsec Kessel Run. What distance, in light-year, does an observer at the finish line measure for the trip? Don't forget to convert parsec to light-year. light-year What distance, in light-year, does Han Solo measure for the trip as he pilots the ship? | light-yearThe Sun orbits around the center of the Milky Way on a circular orbit with a radius of 8 kpc, and at a speed of about 200 km/s.Suppose that the gravitational field of the Milky Way is dominated by a spherical dark matter halo. What is the mass of the halo within the radius of the solar orbit?The energy of a moving object is given by the equation of E-mv². What is the constant? What type of variation is this? If the energy is 16 joules and the mass is 1 kg (kilogram), what is the velocity?