Download Orbital Motion

7.8
Orbits and Harder Circular Motion
(3.3, 3.4)
F = GMm/r2
1) A satellite near the Earth’s surface makes a circular orbit in 90 minutes. The Earth is 6378 km in radius.
A weather satellite completes a circular orbit every 3.5 hours. How far above the Earth’s surface is it?
2) A double star consists of two identical stars, each with a mass of 3.0 x 1030 kg. They are separated by
2.0 x 1011 m between their centres. How long do they take to complete one orbit? (p. 301)
3) A spacecraft has been put in orbit around an asteroid. The asteroid is a spherical rock of radius 15 km
and density of 2600 kg/m3. Calculate the speed of the spacecraft if the orbit has a radius of 300 km.
4) Two remote planets consist of identical material, but one has a radius twice as large as the other. It the
shortest possible period for a low altitude satellite orbiting the smaller planet is 40 minutes, what is it for
the larger planet? (p.301)
5) Roberta Bondar is in a circular orbit above a planet with an altitude equal to the radius of the planet. She
fires her rockets to put herself in a new orbit which has a speed 50% greater than before. What is the
altitude of the new orbit?
6) The acceleration of gravity on Mars is 3.72 m/s2. Mars has a diameter of 6790 km and a period of 24.72
hours. How far away does a satellite have to be so that it remains stationary to an observer on Mars?
7) Two astronauts have tied their spaceships together with a spring that has an unstretched length of1500
m. It has a force constant of 6.7 N/m. The space ships each have a mass of 2500 kg and are orbiting
about their centre of mass with a period of 2.5 minutes. By how much has the cable stretched?
8) A large circus carousel has seats suspended by ropes spinning in a circle. They are 6.2 m from the
ground and are moving in a circle of radius 12.8 m once every 7.5 s. The rope breaks on one swing.
How far does it land from the centre of the carousel?
9) An Australian bushman hunts kangaroos with a rock tied to the end of a 2-m long vine. He holds the
other end 2-m above the ground and swings the rock in a horizontal circle. The vine always breaks when
the angle between the vine and vertical reaches 60o. How close must the hunter get?