Lesson 9: Gravitation

Write your solutions to the following problems and submit them before 6 am on Monday, March 17th.

Submit to the SUBMIT folder on Priscilla or as an attachment to an e-mail message to rfuller@unlinfo.unl.edu or using this Web form.

Numerical Values of various constants for use in gravitational problems:

G = (2/3) × 10-10 N m2/kg2

Mass of Sun = 2.0 × 1030 kg

Mass of Earth = 6.0 × 1024 kg

Mass of Moon = (3/4) × 1023 kg

Mass of Mars = (6.3) × 1023 kg

Earth to Moon distance = (3/8) × 109 m

g at surface of Earth = 10 m/s2

2 = 10

Radius of Sun = 7.0 × 108 m

Radius of Earth = 6.4 × 106 m

Radius of Moon = (1/6) × 107 m

Radius of Mars = (1/3) × 107 m

Earth to Sun distance = 1.5 × 1011 m

Saturn to Sun distance = 1.5 × 1012 m

Your Name:

  1. Using only Newton's law of universal gravitation, the centripetal force law, and the following data:

    at the surface of the Earth, g = 9.8 m/s2

    the radius of the Earth is 6400 km;

    the Moon completes one orbit around the Earth every 27.3 d = 2.40 × 106 s;

    from the Cavendish experiment, G = 6.7 × 10-11 N m2/kg2;

    1. find the mass of the Earth,

    2. find the radius of the Moon's orbit.

  2. Jupiter has a moon with an approximately circular orbit of radius 4.2 × 108 m and a period of 42 h.

    1. What is the magnitude of the gravitational field g due to Jupiter at the orbit of this moon?

    2. From (a) and the value of G, find the mass of Jupiter.

  3. Certain neutron stars are believed to be rotating at about one revolution per second. If such a star has a radius of 30 km, what must be its mass in order that objects on its surface will not be thrown off by the rapid rotation?

  4. Typical satellite orbits around 1960 were 1.6 × 105 m above the Earth's surface--about the minimum altitude required to escape the region of significant atmospheric drag.

    1. What is the potential energy, relative to infinity, of a 1000-kg satellite in such an orbit?

    2. What is its potential energy relative to the Earth's surface?

    3. Find the time that such a satellite requires to complete one orbit.

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