A spaceship travels at a constant speed from earth to a planet orbiting another star. When the spacecraft arrives, 12 years have elapsed on earth, and 9.6 years have elapsed on board the ship. How far away (in meters) is the planet, according to observers on earth? Spaceship departs earth Spaceship arrives at distant planet Number Units
A spacecraft of the Trade Federation flies past the planet Coruscant at a speed of 0.7c. A scientist on Coruscant measures the length of the moving spacecraft to be 76 m. The spacecraft later lands on Coruscant, and the same scientist measures the length of the now stationary spacecraft. What value does she get? meters.
What velocity v must the space shuttle have in order to release the Hubble space telescope in a circular earth orbit d = 640 km about the earth? Answer: v = m/s
A communications satellite is in a synchronous orbit that is 3.6×107 m directly above the equator. The satellite is located between two cities almost on the equator that are separated by a distance of 2.9×106 m. Find the time it takes for a telephone call to go by way of satellite between these cities. Ignore the curvature of the earth. Number Units
On a spacecraft, two engines are turned on for 751 s at a moment when the velocity of the craft has x and y components of v0x = 2730 m/s and v0y = 7020 m/s. While the engines are firing, the craft undergoes a displacement that has components of x = 2.58×106 m and y = 5.88×106 m. Find the (a) x and (b) y components of the craft's acceleration. (a) Number Units (b) Number Units
On a spacecraft, two engines are turned on for 437 s at a moment when the velocity of the craft has x and y components of v0x = 6010 m/s and v0y = 6750 m/s. While the engines are firing, the craft undergoes a displacement that has components of x = 5.21×106 m and y = 7.20×106 m. Find the (a) x and (b) y components of the craft's acceleration. (a) Number Units (b) Number Units
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 455 kg. The spacecraft took 1.04 days to make one complete circular orbit around Eros. Calculate what the mass of Eros must be. Mass of Eros = kg
A mountain located 14.0 km from a person exerts a gravitational force on them equal to 1.00% of their weight. The gravitational constant G is 6.67×10−11 m3/(kg⋅s2), and the acceleration due to gravity 8 at the surface of the Earth is 9.81 m/s2. Calculate the mass M of the mountain. M = kg
From the gravitational law calculate the weight W (gravitational force with respect to the earth) of a 82−kg man in a spacecraft traveling in a circular orbit 214 km above the earth's surface. Express W in both (a) newtons and (b) pounds. Answers: (a) W = N (b) W = Ib
The Sun has a mass of 1.99×10^30 kg. Jupiter has a mass of 1.90×10^27 kg and a mean radius of orbit around the Sun of 7.78×10^8 km. The speed that Jupiter travels in its orbit around the Sun is 1.31×10^4 km/s 4.70×10^4 km/h 4.13×10^5 m/s 4.04×10^2 m/s 1.28×10^4 m/s Other:
A 91 kg person and their 7.5 kg dog are 10 m away from each other. If you approximate them both as perfectly spherical what if the attractive gravitational force between them? Fgrav = N
Suppose you are navigating a spacecraft far from other objects. The mass of the spacecraft is 3.2×104 kg (about 32 tons). The rocket engines are shut off, and you're coasting along with a constant velocity of <0, 28, 0> km/s. As you pass the location < 5, 4, 0 > km you briefly fire side thruster rockets, so that your spacecraft experiences a net force of < 8×105, 0, 0 > N for 23.0 s. The ejected gases have a mass that is small compared to the mass of the spacecraft. You then continue coasting with the rocket engines turned off. Where are you an hour later? (Think about what approximations or simplifying assumptions you made in your analysis. Also think about the choice of system: what are the surroundings that exert external forces on your system? ) r→f = < > m
While passing between Earth and the Moon, a spacecraft is momentarily located on the line connecting the centers of the two bodies and is at a distance of d = 87 km from a radio antenna on the surface of Earth. The distance from the antenna to the moon is denoted by dmoon .
Some scientists have suggested that spacecraft with sails of the kind described in Conceptual Example 4 could be propelled by lasers. Suppose such a sail is constructed of a highly reflective material thin enough so that one square meter of the sail has a mass of just 5.3×10−3 kg. The sail is to be propelled by an ultraviolet laser beam (wavelength = 215 nm) that will strike its surface perpendicularly. (a) Use the impulse-momentum theorem to determine the number of photons per second that must strike each square meter of the sail in order to cause an acceleration of 9.8×10−6 m/s2, which is one million times smaller than the gravitational acceleration at earth's surface. Assume that no other forces act on the sail, and that all the incident photons are reflected. (b) Determine the intensity (power per unit area) that the laser beam must have when it strikes the sail. (a) Number Units (b) Number Units
A satellite is placed in orbit 4.59×105 m above the surface of Jupiter. Jupiter has a mass of 1.90×1027 kg and a radius of 7.14×107 m. Find the orbital speed of the satellite. Number Units
A star rotates in a circular orbit about the center of its galaxy. The radius of the orbit is 2.5×1020 m, and the angular speed of the star is 5.4×10−15 rad/s. How long (in years) does it take for the star to make one revolution around the center? (b) Number Units
A satellite is in a circular orbit around an unknown planet. The satellite has a speed of 1.06×104 m/s, and the radius of the orbit is 1.77 ×106 m. A second satellite also has a circular orbit around this same planet. The orbit of this second satellite has a radius of 9.06×106 m. What is the orbital speed of the second satellite? Number Units
In the Bohr model of hydrogen, the electron moves in a circular orbit around the nucleus. Determine the angular speed of the electron In revolutions per second, when it is in (a) the ground state and (b) the n = 3 state. (a) Number Units (b) Number Units
Two stars M1 and M2 of equal mass make up a binary star system. They move in a circular orbit that has its center at the midpoint of the line that separates them. If M1 = M2 = 1.70 sm (solar mass), and the orbital period of each star is 4.45 days, find their orbital speed. (The mass of the sun is 1.99×1030 kg.) km/s
A spacecraft starts from rest, and makes a journey to a destination 172000 km from its starting point. It does so by accelerating at a constant rate of 8.33 m/s^2 up to the midpoint of the journey, and then decelerates at the same constant rate of 8.33 m/s^2 for the second half of the journey, ending at rest. How long did the entire journey take? 5 hr 44 min 2 hr 52 min 2 hr 31 min 1 hr 47 min
Two people start at the same place and walk around a circular lake in opposite directions. One has an angular speed of 1.68×10−3 rad/s, while the other has an angular speed of 4.14×10−3 rad/s. How long will it be before they meet? Number Units
A star rotates in a circular orbit about the center of its galaxy. The radius of the orbit is 3.8×1020 m, and the angular speed of the star is 2.2×10−15 rad/s. How long (in years) does it take for the star to make one revolution around the center? (b) Number Units the tolerance is +/−2%
A stellar black hole may form when a massive star dies. The mass of the star collapses down to a single point. Imagine an astronaut orbiting a black hole having six times the mass of the Sun. Assume the orbit is circular. (a) Find the speed of the astronaut if his orbital radius is r = 1 AU. m/s (b) Find his speed if his orbital radius is r = 8.9 km. m/s (c) CHECK and THINK: Compare your answers to the speed of light in a vacuum. What would the astronaut's orbital speed be if his orbital radius were smaller than 8.9 km? This answer has not been graded yet.
In the Bohr model of hydrogen, the electron moves in a circular orbit around the nucleus. Determine the angular speed of the electron, in revolutions per second, when it is in (a) the ground state and (b) the n = 4 state. (a) Number Units (b)Number Units
Required information Problem 12.085 - Spacecraft orbiting about the Earth NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. A 500-kg spacecraft first is placed into a circular orbit about the earth at an altitude of 5500 km and then is transferred to a circular orbit about the moon. The mass of the moon is 0.01230 times the mass of the earth and the radius of the moon is 1737 km. Problem 12.085. c - Acceleration of gravity on the moon Determine the acceleration of gravity at the surface of the moon. The acceleration of gravity at the surface of the moon is m/s2.
The first artificial satellite to orbit Earth was Sputnik I (launched by the former Soviet Union in 1957). Its highest point above Earths surface was 963 kilometers, and its lowest point was 210 kilometers (see figure). The center of Earth was at one focus of the elliptical orbit, and the radius of Earth is 6379 kilometers. Find the eccentricity of the orbit. x = 210 km, y = 963 km a. Eccentricity: e ≈ 0.134 b. Eccentricity: e ≈ 0.074 c. Eccentricity: e ≈ 0.114 d. Eccentricity: e ≈ 0.094 e. Eccentricity: e ≈ 0.054
Two satellites are in circular equatorial orbits of different altitudes. Satellite A is in a geosynchronous orbit (one with the same period as the earth's rotation so that it "hovers" over the same spot on the equator). Satellite B has an orbit of radius rB = 28000 km. Calculate the velocity which A appears to have to an observer fixed in B when the elevation angle θ is (a) 0 and (b) 90∘. The x-y axes are attached to B, whose antenna always points toward the center of the earth (-y-direction). Answers: (a) θ = 0: vrel = km/h (b) θ = 90∘: vrel = km/h
A spacecraft with mass 2070 kg is in circular orbit around Earth as shown with the green circle in the figure, at an altitude h = 690 km. What is the period of the orbit? Reminder: the radius of the orbit is the altitude plus RE, the radius of Earth. RE = 6.371×103 km. For reference, the mass of Earth, ME, is 5.98×1024 kg. T = s At point P in the orbit (see figure), the spacecraft reduces its speed by 1.7%, causing it to be in an elliptical orbit. What is the kinetic energy of the ship immediately after this slowing? (Note that the potential energy of orbit will not have changed since it is still at point P ). K = J [Note: use exponential notation to enter your answer: "9.99 e12" represent 9.99×1012. ] What is the semi-major axis of the new (elliptical) orbit? a = km What is the perigee distance for the new (elliptical) orbit? Rp = km
A planet is in an elliptical orbit around a distant star. At periastron (the point of closest approach to the star), the planet is rp = 4.30×108 km from the star and is moving with a speed of vp = 18.5 km/s. When the planet is at apastron (the point of greatest distance from the star), it is ra = 8.70×108 km from the star. How fast is the planet moving at apastron? va = km/s
The Xanthar mothership locks onto an enemy cruiser with its tractor beam (see the figure below); each ship is at rest in deep space with no propulsion following a devastating battle. The mothership is at x = 0 when its tractor beams are first engaged, a distance d = 245 xiles from the cruiser. Determine the x-position in xiles (measured from x = 0 ) of the two spacecraft when the tractor beam has pulled them together. Model each spacecraft as a point particle with the mothership of mass M = 160 xons and the cruiser of mass m = 16.0 xons. xiles
A space vehicle describing a circular orbit at a speed of 24×103 km/h releases its front end, a capsule that has a gross mass of 600 kg, Including 400 kg of fuel as shown in the figure. The fuel is consumed at the rate of 16.5 kg/s and ejected with a relative velocity of 2925 m/s. Determine the maximum speed attained by the capsule. The maximum speed attained by the capsule is ×103 km/h.
A spacecraft is on a journey to the moon. At what point, as measured from the center of the earth, does the gravitational force exerted on the spacecraft by the earth balance that exerted by the moon? This point lies on a line between the centers of the earth and the moon. The distance between the earth and the moon is 3.85×108 m, and the mass of the earth is 81.4 times as great as that of the moon. Number Units
A spacecraft with a proper length of 300 m passes by an AMT observer on the Earth. According to this observer, it takes 0.750 μs for the spacecraft to pass a fixed point. Determine the speed of the spacecraft as measured by the Earth-based observer. A spacecraft with a proper length of Lp passes by an observer S on the Earth. According to this observer, it takes a time interval Δt for the spacecraft to pass a fixed point. Determine the speed of the object as measured by the Earth-based observer.
The space shuttle A is in an equatorial circular orbit of 371-km altitude and is moving from west to east. Determine the velocity and acceleration which it appears to have to an observer B fixed to and rotating with the earth at the equator as the shuttle passes overhead. Use R = 6378 km for the radius of the earth and use g = 9.814 m/s2. Answers: vrel = km/h arel = m/s2
The planet Neptune moves in an elliptical orbit with the sun at one focus. Given that Neptune's closest approach to the sun is approximately 4444.45 million kilometers and that the eccentricity of Neptune's orbit is approximately 0.011 , estimate this planet's maximum distance from the sun. Express your answer as a decimal rounded to two decimal places. Answer How to enter your answer (opens in new window) million kilometers
Two stars in a binary system orbit around their center of mass. The centers of the two stars are 7.38×1011 m apart. The larger of the two stars has a mass of 3.60×1030 kg, and its center is 1.91×1011 m from the system's center of mass. What is the mass of the smaller star?
Astronomers discover an exoplanet, a planet orbiting a star other than the Sun, that has an orbital period of 2.50 Earth years in a circular orbit around its star, which has a measured mass of 3.50×1030 kg. Determine the radius r of the exoplanet's orbit. r = m
A planet of mass m = 9.35×1024 kg orbits a star of mass M = 2.35×1029 kg in a circular path. The radius of the orbit is R = 1.45×107 km. What is the orbital period Tplanet of the planet in Earth days? Tplanet = days
The Earth's orbit around the Sun has a semimajor axis of 1.496×108 km and an eccentricity of 0.01671 . The speed of the Earth at perihelion is 30.29 km/s. What is its speed (km/s) at aphelion? 32.32 29.29 31.30 27.83 30.27 29.78 30.03 28.45 26.74 28.11
A spacecraft is traveling with a velocity of v0x = 4990 m/s along the +x direction. Two engines are turned on for a time of 947 s. One engine gives the spacecraft an acceleration in the +x direction of ax = 2.32 m/s2, while the other gives it an acceleration in the +y direction of ay = 8.34 m/s2. At the end of the firing, what is a) vx and b)vy ? (a) Number Units (b) Number Units