## A triumph for Newtonian gravity

As children of our age, we find it natural to think of the planets as cousins of the Earth remote and taciturn, perhaps, but cousins nevertheless. To visit them is not a trip lightly undertaken, but we and our robots have done it. Men have walked on the Moon live television pictures from Mars, Jupiter, Saturn, Uranus, and Neptune have graced millions of television screens around the world and we know now that there are no little green men on Mars (although little green bacteria are not...

## The inescapable force

No matter where you go, you can't seem to escape it. Pick up a stone and feel its weight. Then carry it inside a building and feel its weight again there won't be any difference. Take the stone into a car and speed along at 100 miles per hour on a smooth road again there won't be any noticeable change in the stone's weight. Take the stone into the gondola of a hot-air balloon that is hovering above the Earth. The balloon may be lighter than air, but the stone weighs just...

## Vorbit gR1231

Given that the circumference of the satellite's orbit is 40 000 km, one orbit at this speed will take 5100 s, or 84 minutes. Since we have used values of g and R appropriate to the surface of the Earth, the true period of a typical near-Earth orbit at 300 km altitude is a bit longer, more like 91 minutes. (Geostationary orbits are much higher see Chapter 4.) We can solve Equation 3.1 for the acceleration g by squaring and dividing by R. If we change the symbol for acceleration to a (which will...

## Info

A more sophisticated and accurate orbit program This investigation is for readers who want to learn some of the ingenious methods by which computer experts improve the accuracy of computer programs. We will explore two improvements. One is to improve the accuracy of each time-step, and the other is to control the accuracy of each time-step. (a) Improving accuracy. Recall that in Chapter 1, we found that the most sensible approximation to the change in the position of a body...

## Cambridge University Press

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title www.cambridge.org 9780521455060 Bernard Schutz 2003 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place...

## Enlargement of Moon

This part of the Moon is further from the Earth, so is pulled less strongly, and slightly backwards in its orbit. This part of the Moon is closer to the Earth, so is pulled more strongly, and slightly forwards in its orbit. Figure 5.5. How tidal forces led the Moon to show the same face to the Earth at all times. The Moon's bulge lagged behind the tidal forces when it was spinning rapidly, leading to an elliptical shape that did not point towards the Earth. All rotations in this diagram are...

## R

Exercise 6.2.1 Solving the quadratic equation The general solution of the quadratic equation ax2 bx c 0 for x is b 1 2 1 2 x - b2 - 4ac , 6.17 where the sign indicates that there are two solutions, found by taking either sign in the expression. Apply this formula to solve the quadratic equation above for R2. Show that the two roots are R1 and the root given by Equation 6.14. Exercise 6.2.2 Getting from the Earth to other planets Use Equation 6.16 to calculate the speed needed to go from the...