BackYou have been visiting a distant planet. Your measurements have determined that the planet's mass is twice that of earth but the free-fall acceleration at the surface is only one-fourth as large. What is the planet's radius?
(I) What is the weight of a 74-kg astronaut in outer space traveling with constant velocity?
(II) What is the apparent weight of a 75-kg astronaut 2800 km from the center of the Moon in a space vehicle accelerating toward the Moon at 1.8m/s2? State “direction” in each case.
(III) Two identical particles, each of mass m, are located on the x axis at x= +x0 and x = -x0. Determine a formula for the gravitational field due to these two particles for points on the y axis; that is, write g as a function of y, m, x0, and so on.
(III) Two identical particles, each of mass m, are located on the x axis at x= +x0 and x = -x0. At what point (or points) on the y axis is the magnitude of g a maximum value, and what is its value there? [Hint: Take the derivative dg/dy.]
The rings of Saturn are composed of chunks of ice that orbit the planet. The inner radius of the rings is 73,000 km, and the outer radius is 170,000 km. Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn’s own rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 x 1026.
Jupiter is about 320 times as massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter because people cannot survive more than a few g’s. Calculate the number of g’s a person would experience at Jupiter’s equator, using the following data for Jupiter: mass = 1.9 x 1027 kg, equatorial radius = 7.1 x 104 km, rotation period = 9 hr 55 mins. Take the centripetal acceleration into account.
A particle is released at a height rE (radius of Earth) above the Earth’s surface. Determine its velocity when it hits the Earth. Ignore air resistance. [Hint: Use Newton’s second law, the law of universal gravitation, the chain rule, and integrate.]
The Near Earth Asteroid Rendezvous (NEAR) spacecraft, after traveling 2.1 billion km, orbited the asteroid Eros with an orbital radius of about 20 km. Eros is roughly 40km x 6km x 6km. Assume Eros has a density (mass/volume) of about 2.3 x 103 kg/m3. What would g be at the surface of a spherical Eros?