Pre-AP Physics
Newton’s Universal Law of Gravitation, Satellites
1. A hydrogen atom consists of a proton of mass 1.67×10-27 kg and an orbiting electron of mass 9.11×10-31 kg. In one of its orbits, the electron is 5.3×10-11 m from the proton. What is the mutual attractive force between the proton and electron? (Ans. 3.6 X 10−47 N)
2. The mass of the moon is 7.4×1022 kg and its mean radius is 1.75×103 km. What is the acceleration due to gravity at the surface of the moon? (Ans. 1.6 m/s2)
3. The gravitational force between two masses is F. What is the gravitational force if the masses are moved to a) twice their initial distance and b) one half their initial distance?
4. A satellite orbits Mars at distance above its surface equal to three times the radius of Mars. What is the acceleration of gravity of the satellite when compared to the acceleration of gravity on the surface of Mars?
5. A hypothetical planet has mass that is twice that of Earth and a radius that is one-half that of Earth. What is the acceleration due to gravity on the planet in terms of g, the acceleration due to gravity on Earth?
6. An object weighs 432 N on the surface of the Earth. The earth has radius r. If the object is raised to a height of 3r above the Earth’s surface, what is it weight at this location? (Ans. 27 N)
7. A satellite is in a low circular orbit about the Earth. (i.e. it just skims the surface of the Earth. Watch your head!) The mass of the Earth is 5.98×1024 kg and the mean radius of the earth is 6.38×106 m. a) What is the speed of the satellite? (Ans. 7910 m/s) b) How long does it take (in minutes) to make one revolution about the earth? (Ans. 84.5 min)
8. A small satellite moving in a circular orbit about a spherical planet with mass M. The height of the satellite above the surface of the planet is 2r where r is the radius of the planet. Derive and expression for the satellite’s orbital velocity.
9. Europa, (an excellent name for one of your future daughters) a moon of Jupiter, has an orbital diameter of 1.34×109 m and a period of 3.55 Earth days. Find the mass of Jupiter. (Ans. 3.07 X 105 s)