# The Solar System is held together by gravity

 BikiCrumbs: The Solar Syst…ther by gravity

## Students learn to:

#### 1. describe a gravitational field in the region surrounding a massive object in terms of its effects on other masses in it

Massive objects have gravitational fields and they tend to exert a force of attraction on other objects. It will also exert a centripetal force, which causes objects to orbit around it.

Gravity is a force of attraction between any two masses. The heavier the masses the larger the gravitational force. This force is proportional to $\frac {1}{d^2}$ meaning that the field extends to infinity, the affect however becomes less with distance.

#### 2. define Newton’s Law of Universal Gravitation: $F = G \frac {m_1 m_2}{d^2}$

It states that the gravitational attraction between two objects is directly proportional to the product of their masses and is inversely proportional to the square of the distance between them. This is then multiplied by the gravitational constant ($6.7 \times 10^{-11}$)

$F = G \frac {m_1 m_2}{d^2}$

#### 3. discuss the importance of Newton’s Law of Universal Gravitation in understanding and calculating the motion of satellites

Satellites must have a certain velocity in order to stay in orbit. If not they will either crash into earth or go out into space and never return. This velocity depends on the force of gravity acting on the satellite. Satellites paths of motion are affected by gravity, this can be seen by orbits and the slingshot affect.

The law of universal gravitation can be useful to derive the following two equations, which are useful to calculate the motion of satellites:

#### 4. identify that a slingshot effect is provided by planets for space probes

The slingshot effect involves a probe approaching a planet into a hyperbolic orbit to gain kinetic energy from the planet’s gravitational field. This works because as the probe approaches the planet it is swung around by gravity. The net effect is that the planet loses kinetic energy as the probe gains some.

The slingshot effect allows satellites to change speed and direction. The change in direction is due to the gravitational field which applies a force to the space probe which changes its direction. The change in speed is because, relative to the sun, the passing space probe has gained velocity from the moving planet.

Change in Direction:

Change in Speed:

Note 1: If the planet was stationary then this attraction would slow the space probe and cancel out the attraction that initially occurred, thus no increase in speed would be present, however the planet is orbiting the sun, so the distance between the space probe and the planet is larger this greater distance means that the force of gravity is less and only some of this force is cancelled out by the initial attraction. Hence the speed of the space probe has increased.

## Students

#### 1. present information and use available evidence to discuss the factors affecting the strength of the gravitational force

From the formula, , the factors that affect gravitational force are Universal Gravitational Constant, mass of both bodies and the distance separating these two bodies.

In regards to the gravitational force on Earth the factors include (but are not limited to):

• Mass of Earth
• Radius of earth (also the altitude you are at) (ie. g which equals 9.8ms-2 on earth will vary depending on your altitude)
• Distribution of mass density on Earth (this includes large mountains, etc. and the nature various of mass density around the Earth)
• The moon and other close large masses (this is seen by the tides)