Gravitation | Notion

This topic is contained in pages $52-74$ of the textbook.

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An astronomical unit (AU) is a unit of measurement defined using the mean distance from the centre of the Earth and the centre of the Sun, $1.5 \times 10^{11} \space m$ (data sheet).

A light year is a unit of astronomical distance equivalent to the distance that light travels in one year.

→ $s=ct=3.00 \times 10^8\times 365.25 \times 24 \times 60 \times 60=9.467\times10^{15}\space m$

The definition of gravitational field strength is the gravitational force acting on a unit mass.

$$ g=\dfrac{F}{m} $$

The following relationship can be used to carry out calculations involving gravitational force, masses and their separation.

$$ F=\dfrac{GMm}{r^2} $$

The following relationships can be used to carry out calculations involving period of satellites in circular orbit, masses, orbit radius, and satellite speed.

$$ F=\dfrac{GMm}{r^2}=\dfrac{mv^2}{r}=mr\omega^2=mr(\dfrac{2\pi}{T})^2 $$

The region of space around an object where it can exert a gravitational force on another object placed in that space is called the gravitational field. These are shown diagrammatically using field lines.

Field lines around singular astronomical object.

Field lines around system involving two astronomical objects.

Gravitational field lines skew to the object with larger mass — the null point is closer to the object with smaller mass.

The definition of the gravitational potential of a point in space is the work done in moving unit mass from infinity to that point.

The energy required to move mass between two points in a gravitational field is independent of the path taken.

The following relationships can be used to carry out calculations involving gravitational potential (measured in $J \space kg^{-1}$), gravitational potential energy, masses and their separation.

$$ V=-\dfrac{GM}{r} $$

$$ E_P=Vm=-\dfrac{GMm}{r} $$