a) We send a probe to orbit a nearby asteroid and take some pictures of it. The probe enters an orbit that puts it 850m from the centre of the asteroid. If the probe moves at 12m/s, determine the mass of the asteroid
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- Hunting a black hole. Observations of the light from a certain star indicate that it is part of a binary (two-star) system. This visible star has moves in a circle of radius r1 and has orbital period T. Variations in the brightness of nearby stars suggest that the unseen companion moves in a circle of radius r2 (see the figure). Find the approximate masses (a) m1 of the visible star and (b) m2 of the dark star. Express your answer in terms of r1, r2, T, and G. I asked this question before and recieved an incorrect answer, so I'm asking again.After the NEAR spacecraft passed Mathilde, on several occasions rocket propellant was expelled to adjust the spacecraft's momentum in order to follow a path that would approach the asteroid Eros, the final destination for the mission. After getting close to Eros, further small adjustments made the momentum just right to give a circular orbit of radius 45 km (45 × 103 m) around the asteroid. So much propellant had been used that the final mass of the spacecraft while in circular orbit around Eros was only 550 kg. The spacecraft took 1.04 days to make one complete circular orbit around Eros. Calculate what the mass of Eros must be.When an object is orbit around a planet, what is it actually going on? The force of Earth's gravity pushes outward and keeps the object from falling. Gravity, combined with the satellite's momentum, cause the satellite to stay orbit above Earth, instead of falling back down to the ground. These forces must be in balance to maintain an orbit. The object starts to have no mass, and therefore can stay in orbit. When the object is in orbit, gravity no longer acts upon that object, and therefore can maintain its constant circular path without a influence of an outside force.
- A binary star consist of two stars of the same mass m revolving in a circle of radius R about their common centre of mass. Suppose that a meteorite passes through the centre of mass of the binary star in a direction perpendicular to the orbital plane. What is the minimum speed that the meteorite must have at the centre of mass in order for it to escape from the gravitational attraction of the binary star? ANSW: 4Gm R wA meteoroid is moving towards a planet. It has mass m = 0.22×109 kg and speed v1 = 3.5×107 m/s at distance R1 = 2.9×107 m from the center of the planet. The radius of the planet is R = 0.46×107 m. The mass of the planet is M = 3.2×1025 kg. There is no air around the. Calculate the value of v in meters per second.A meteoroid is moving towards a planet. It has mass m = 0.54×109 kg and speed v1 = 4.7×107 m/s at distance R1 = 1.6×107 m from the center of the planet. The radius of the planet is R = 0.78×107 m. The mass of the planet is M = 5.6×1025kg. There is no air around the planet. a)Enter an expression for the total energy E of the meteoroid at R, the surface of the planet, in terms of defined quantities and v, the meteoroid’s speed when it reaches the planet’s surface. Select from the variables below to write your expression. Note that all variables may not be required.α, β, θ, d, g, G, h, m, M, P, R, R1, t, v, v1 b)Enter an expression for v, the meteoroid’s speed at the planet’s surface, in terms of G, M, v1, R1, and R. c)Calculate the value of v in meters per second.
- Two planets P₁ and P₂ orbit around a star S in circular orbits with speeds v₁ = 43.4 km/s, and v₂ = 57.0 km/s respectively. If the period of the first planet P₁ is 790 years what is the mass, in kg, of the star it orbits around? kg Determine the orbital period, in years, of P2. yrThe solar system is 25,000 light years from the center of our Milky Way galaxy. One light year is the distance light travels in one year at a speed of 3.0×108m/s. Astronomers have determined that the solar system is orbiting the center of the galaxy at a speed of 230 km/s. The approximate mass of the galactic center was calculated to be 1.88*1041 kg. Assume that the sun is a typical star with a typical mass. If galactic matter is made up of stars, approximately how many stars are in the center of the galaxy? Note : Astronomers have spent many years trying to determine how many stars there are in the Milky Way. The number of stars seems to be only about 10% of what you'll find in part d. In other words, about 90% of the mass of the galaxy appears to be in some form other than stars. This is called the dark matter of the universe. No one knows what the dark matter is. This is one of the outstanding scientific questions of our day.Problem 9: A 3500-kg spaceship is in a circular orbit 180 km above the surface of Earth. It needs to be moved into a higher circular orbit of 390 km to link up with the space station at that altitude. In this problem you can take the mass of the Earth to be 5.97 x 1024 kg.
- White dwarf stars are produced by the collapse of regular stars, such as our sun, toward the end of their normal life. Suppose a star initially has the same mass as our sun and the same radius as that of the sun. Suppose further that it collapses into a white dwarf with a radius of 5000km. If the initial period of the star is the same 27 day period of our sun, what is the resulting period of the white dwarf?5) Two neutron stars are separated by a distance of 2.98x10^(10)m. Both have a mass of 3.17x10^(30)kg and a radius of 253000m. They are initially at relative rest. a) What is the speed of both when the distance between them is half the initial value? in m/s b) What is the speed of both when they are about to collide? in m/sA binary-star system contains a visible star and a black hole moving around their center of mass in circular orbits with radii r1 and r2 , respectively. The visible star has an orbital speed of v=5.36x105 ms-1 and a mass of m1 =5Ms ,where Ms= 1.98x1030kg is the mass of our Sun. Moreover, the orbital period of the visible star is T = 30 hours.(a) What is the radius r1 of the orbit of the visible star?(b) Calculate the mass m2 of the black hole in terms of MS . [Hint: One root of the equation x3 = 20a(5a+x)2 , where a is a constant, is x = 28a .]