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Chapter 8: Problem 1

What do Newton's apple and the Moon have in common?

Short Answer

Expert verified
Newton's apple and the Moon have in common the fact that they are both influenced by gravity. The apple falls to the ground because it is attracted by the Earth's gravity. Similarly, the Moon is kept in orbit around the Earth due to the gravitational pull between the Earth and the Moon. So, both are experiencing the effects of gravity, as described by Newton's law of universal gravitation.

Step by step solution

01

Understanding the Gravity

Newton's law of universal gravitation states that every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This statement means that the size and direction of the force \(F\) equals the mass of one object (in this case, Newton's apple or the Moon) times the mass of another object, divided by the distance between them squared, and then multiplied by the gravitational constant \(G\).
02

Applying Law of Gravitation to Newton's Apple

When an apple falls from a tree, it is attracted towards the center of the earth due to the gravity between them. The force acting upon the apple is the product of the mass of the apple, the mass of the earth and the gravitational constant, divided by the square of the distance between them.
03

Applying Law of Gravitation to the Moon

Similarly, the moon is continuously falling towards the Earth. It does not actually hit the Earth because it also has a tangential velocity, which means it moves at a right angle to the force of the Earth's gravity. This allows it to fall around the Earth, in a circle or ellipse, rather than straight into it.

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Most popular questions from this chapter

A friend who knows nothing about physics asks what keeps an orbiting satellite from falling to Earth. Give an answer that will satisfy your friend.

Spacecraft that study the Sun are often placed at the so-called \(L 1\) Lagrange point, located sunward of Earth on the Sun-Earth line. L1 is the point where Earth's and Sun's gravity together produce an orbital period of one year, so that a spacecraft at L1 stays fixed relative to Earth as both planet and spacecraft orbit the Sun. This placement ensures an uninterrupted view of the Sun, without being periodically eclipsed by Earth as would occur in Earth orbit. Find LI's location relative to Earth. (Hint: This problem calls for numerical methods or solving a higher-order polynomial equation.)

Space explorers land on a planet with the same mass as Earth, but find they weigh twice as much as they would on Earth. What's the planet's radius?

Why are satellites generally launched eastward and from low latitudes? (Hint: Think about Earth's rotation.)

What's the approximate value of the gravitational force between a \(67-\mathrm{kg}\) astronaut and a \(73,000-\mathrm{kg}\) spacecraft when they're \(84 \mathrm{m}\) apart?
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