Conceptual Questions:
1. A satellite in orbit about the Earth encounters a slight, but not zero, air resistance. Does this friction cause the satellite to slow down? Consider all forms of energy.
2. What are the general principles needed to consider when calculating the orbit period of a satellite around a planet? How can we use a measured orbit period and distance to find the mass of the planet?
Numerical Problems:
Notes: keep in mind the difference between the surface acceleration of gravity g and the gravitation constant G; a useful formula is g = GM/R2 where M and R are the mass and radius of a planet, respectively. The acceleration caused by gravity at any distance r outside the planet is ag = GM/r2. Also keep in mind the formulae for cetripetal acceleration, a =v2/r = w2r.
1. Of the nine known planets in our solar system, the innermost is Mercury. When compared to the other planets in the system, Mercury has the:
a. greatest centripetal acceleration
b. greatest period of revolution
c. smallest angular velocity
d. smallest tangential velocity
2. An object of mass 0.5 kg is transported to the surface of Planet X where the object's weight is measured to be 20 N. The radius of the planet is 4 x106 m. What is the mass of Planet X? (G = 6.67 x10-11 N-m2/kg2)
3. An object of mass 0.5 kg is transported to the surface of Planet X where the object's weight is measured to be 20 N. The radius of the planet is 4 x106 m. What free fall acceleration will any object experience when at the surface of Planet X?
4. An Earth satellite is orbiting at a distance from the Earth's surface equal to one Earth radius (4000 miles). At this location, the acceleration due to gravity is what factor times the value of g at the Earth's surface?
5. A satellite is in a circular orbit about the Earth at a distance of one Earth radius above the surface. What is the velocity of the satellite (The radius of the Earth is 6.4 x106 m and G = 6.67 x10-11 N-m2/kg2)?
6. A cylindrical space colony 8 km in diameter and 30 km long has been proposed as living quarters for future space explorers. Such a habitat would have cities, land and lakes on the inside surface and air and clouds in the center. All this would be held in place by rotation of the cylinder about the long axis. How fast would such a cylinder have to rotate to produce a 1-g "gravitational field" at the walls of the cylinder?
7. If the mass of Mars is 0.107 times that of Earth and its radius is 0.53 that of Earth, what is the gravitational acceleration g at the surface of Mars?
8. Geosynchronous satellites orbit the Earth at a distance from the Earth's center such that their angular velocity at this height is the same as the rotation of the Earth. Thus they appear stationary at certain locations in the sky. What value should this distance have?