An average-sized asteroid located 5.0 x 107km from Earth with mass 2.0 × 10¹³ kg is detected headed directly toward Earth with speed of 2.0 km/s. What will its speed be just before it hits our atmosphere? (You may ignore the size of the asteroid.)
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- An average-sized asteroid located 7.4 ✕ 107 km from Earth with mass 2.5 ✕ 1013 kg is detected headed directly toward Earth with speed of 8.0 km/s. What will its speed be (in km/s) just before it hits our atmosphere? (You may ignore the size of the asteroid. Assume the height of our atmosphere is 100 km.)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.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 w
- Consider the observation that the acceleration due to the gravitational force acting on a mass around a host planet decreases with the square of the separation between the objects. We can ask ourselves: why is it still accurate to consider a gravitational acceleration value of 9.8\frac{m}{s^2}9.8s2m for all of our projectile motion problems and all of our gravitational potential energy from prior modules? Let's analyze a situation and justify this analysis method: consider an object being launched from ground level to an altitude of 10,000 meters, roughly the cruising altitude of most jet liners, and far above our everyday experiences on Earth's surface. Compare the gravitational acceleration of the object at Earth's surface (the radius of Earth is about r_E=6.37\times10^6mrE=6.37×106m) to the acceleration value at the 10,000 meter altitude by determining the following ratio: g10,000m/gsurfaceA 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.
- A 1000 kg object is found heading towards the Earth. At the moment it is 4 Earth radii away from the surface of our planet the asteroid is moving at 100 m/s. If it collides with our planet, how fast will it be moving right before it hits the surface? How much kinetic energy is going to be released in this collision?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/sThe radius of Venus (from the center to just above the atmosphere) is 6050 km (6050x103 m), and its mass is 4.9x1024 kg. An object is launched straight up from just above the atmosphere of Venus. (a) What initial speed is needed so that when the object is far from Venus its final speed is 3000 m/s? Vinitial = 10100 X m/s (b) What initial speed is needed so that when the object is far from Venus its final speed is 0 m/s? (This is called the "escape speed.") Vescape = m/s
- If a Saturn V rocket with an Apollo spacecraft attached had a combined mass of 2.6 × 105 kg and reached a speed of 12 km/s, how much kinetic energy would it then have?After consuming all of its nuclear fuel, a massive star can collapse to form a black hole, which is an immensely dense object whose escape speed is greater than the speed of light. Newton's law of universal gravitation still describes the froce that a black hole exerts on objects outside it. A spacecraft in the shape of a long cylinder has a length of 100m, and its mass with occupants is 1000kg. It has strayed too close to a black hole having a mass 100 times that of the sun. If the nose of the spacecraft points toward the center of the black hole, and if the distance between the nose of the spacecraft and the black hole's center is 10km (a) determine the total force on the spacecraft. (b) What is the difference in the force per kilogram of mass felt by the occupants in the nose of the ship versus those in the rear of the ship farthest from the black hole?What is the escape speed on the surface of Neptune? (the mass of Neptune is 1.02 x 1026 kg and the radius o Neptune is 2.48 x 10’m)