{{jcomments on}jatex options:inline}\frac{GM_{Sun} m_{Earth}}{r^2}= \frac{m_{Earth} v^2}{r}{/jatex}

Rearranging gives {jatex options:inline}M_{Sun} = \frac{v^2r}{G}{/jatex}

The Earth orbits the Sun once a year or 365 days. In a year there are {jatex options:inline}365 \times \ 24 \times 60^2 = 31536000 s{/jatex}

The Earth orbits the Sun at a radius of {jatex options:inline}150 \times 10^9 m{/jatex}

The speed of the Earth around the Sun is {jatex options:inline}v= \frac{2 \pi r}{T} = \frac{2 \pi \times 150 \times 10^9}{31536000}=29.885 \times 10^3 m/s 29.995 m/s{/jatex}

The mass of the Sun is then {jatex options:inline}M=\frac{29885^2 \times 150 \times 10^9}{6.67 \times 10^{-11}} = 2.01 \times 10^30 kg{/jatex}

This is an estimate. The main errors arise because we have made the following approximation

Both the Sun and the Earth are spheres.

The orbit of the Earth is a circle.

The mass of the Earth is small compared with the Sun so can be ignored.

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Magnetic materials are called 'ferrous', and magnetism can be induced in them. Iron, cobalt and nickel are ferrous. Magnetic come in hard and soft varieties. Soft magnetic materials are easily magnetized and easily demagnetized. The best example is iron, which because of this property is commonly used in loudspeakers and electric locks. Hard magnetic material hard hard to magnetize and hard to demagnetize.

Hard magnetic materials, including many types of steel, can be used to make permanent magnets, which do not lose their magnetism easily when the inducing field is taken away.

The coercive force is a measure of the external inducing field need to induce a certain amount of residual magnetism, shown on the vertical axis. It is larger for the hard magnetic material.]]>

2. Placed inside a solenoid with a direct current moving through it.

3. Magnetic materials are often weakly magnetised because of the Earths own magnetic field.

A magnet may be demagnetised by

1. Hammering it repeatedly to disrupt the magnetic domain structure.

2. Heating it.

3. Place it inside a solenoid with ac current flowing through it.]]>

Hence {jatex options:inline}v=\sqrt{\frac{GM}{r}}{/jatex}

As the radius of the orbit increases the speed of the planet decreases. The kinetic energy decreases, but because the total energy (kinetic plus gravitational potential energy is negative and equal to half the gravitational potential energy {jatex options:inline}GPE= - \frac{GM_{Sun} m_{Earth}}{r}{/jatex}) the total energy of the planet will increase.

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{jatex options:inline}\frac{m_{Aircraft}v^2}{r} = \frac{GM_{Earth}m_{Aircraft}}{r}{/jatex}

Cancel {jatex options:inline}m_{Aircraft}{/jatex}

{jatex options:inline}\frac{v^2}{r} = \frac{GM_{Earth}}{r^2}{/jatex}

Multiply by {jatex options:inline}r{/jatex} and square root.

{jatex options:inline}v=\sqrt{\frac{GM_{Earth}}{r}} = \sqrt{\frac{6.67 \times 10^{-11} \times 5.98 \times 10^{24}}{6370000 + 96540}} = 7853 m/s{/jatex}

This is about 24 times the speed of sound at sea level.

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