Instruction

1

Attempts to measure

**the distance**from the Earth to**the Sun**were made in Ancient Greece (Aristarchus of Samos), but to call them accurate was difficult. In the XVII century this**distance**was measured using the method of parallax (difference of position of an object relative to a subject based on the position of the observer). Was determined as the horizontal parallax**of the Sun**is the angle with**the Sun**located on the horizon, is visible perpendicular to the line of sight radius of the Earth. Further research was based on the length of the radius of the Earth.2

In 1672, it was determined

**the distance**from earth to Mars, who at that time was located in the diametrically opposite point of the Sun. The trigonometric laws that allow to calculate the relative distances of the planets, expressed in fractions of the distance Earth-Sun, was known, and with their help, it was computed the actual**distance**from**the Sun**to the Earth. At that time it was the most accurate value of 138.5 million kilometers.3

Subsequently, the astronomical unit was trying to determine many times, taking as a basis of computing

**the distance**from Earth to Venus, but because observers were quite a lot, and the dimensions were of high complexity, the inconsistency in the obtained values was very large. In the late nineteenth century by measuring displacement of the apparent positions of the stars was computed a more accurate value 149, 5 million kilometers.4

The second half of the XX century brought the scientific and technical revolution, and with it the development of radio. That is the radar method (in which in the direction of a celestial body send short impulse, take the reflected signal and based on the speed of propagation and the transit time of the signal in both directions to determine

**the distance**to this body) allowed to calculate the**distance**from Earth to**the Sun**as accurately as possible at different times of the year and take an average value equal to 149 597 870 km.# Advice 2 : How to determine the distance to the object

The ability to determine

**distance**to objects on the ground can be useful in a variety of situations. For accurate and rapid determination of distances, there are special devices (range finders, scales, binoculars, rifle scopes and telescope). However, even without special tools, you can learn to find**distance**with simple available tools.You will need

- A matchbox, a pencil, a ruler

Instruction

1

The most simple way to determine

**distance**on the ground is associated with the use of eye. The main thing here – trained visual memory and the ability to mentally postpone into the visible area constant measure of length, e.g. 50 or 100 m. Fix memory benchmarks and compare them the**distance**that you should measure on the ground. One of the simplest standards, the**distance**between the electricity poles, which is usually about 50 m.2

Measuring

**distance**by mental snooze permanently, keep in mind that the local objects will appear to be reduced according to remove them. In other words, if you delete two times the object seems to be twice smaller.3

When using the eye keep in mind that in conditions of poor visibility (fog, dusk, cloudy weather, rain, etc.) objects seem to be located farther than the really are. The accuracy of this method primarily depends on the training of the observer. A common mistake in distance in kilometer is about 15%.

4

Use the method of determining distances on the linear dimensions. To do this, take a ruler and hold it at arm's length. Measure with a ruler in millimeters viewable width (height)

**of the object**to which the measuring**distance**. The actual width and height of the object, known to you, turn to centimeters, then divide by the apparent size in millimeters, and multiply the result by 6 (a constant value). The result is the required**distance**m from**the object**.5

The third way to determine

**distance**on the ground – the angular size. This requires to know the linear size**of the object**(length, height or width) and the angle in mils, at which the observed object is visible. With this background, determine**a distance**to**the object**according to the formula:D = L x 1000 / A;where D is**distance**to**object**; L — linear size of**object**; A — the angle at which the visible linear size**of the object**; 1000 is a constant.6

For determining the angular magnitude should know that the segment length of 1 mm, located at a distance of 50 cm from the eye will correspond to the angle of 2 mils. Accordingly, for a length of 1 cm the angular size is equal to 20 thousandths and so on. Remember the angular size (in thousandths) of some available tools:the thumb (thickness) – 40;

Pinky (thickness) – 25;

Pencil 10-11;

Matchbox (width) – 50;

Matchbox (height) - 30

Match (thickness) – 2.

Pinky (thickness) – 25;

Pencil 10-11;

Matchbox (width) – 50;

Matchbox (height) - 30

Match (thickness) – 2.

# Advice 3 : How to determine the distance to planets

Despite the fact that most close from us

**planets**extremely far from Earth,**distance**it is of ultimate importance. And if so, it can be determined. And this was first done a long time ago – in the days of the Ancient Greek astronomer, mathematician and philosopher Aristarchus from the island of Samos proposed a method of determining the distance to the moon and its size. How can you determine**the distance**to planets? The method is based on the phenomenon of parallax.You will need

- calculator;
- - radar;
- - stopwatch;
- - Handbook of astronomy.

Instruction

1

Radar is one of the modern methods of determining the distance from Earth to the planets (geocentric distance). It is based on a comparative analysis of the sent and reflected signal.Send a radio signal in the direction of interest

**of the planet**and turn on the stopwatch. When will the reflected signal to stop the clock. By the known velocity of propagation and the time during which the signal reaches**the planet**is reflected, calculate the**distance**to**the planet**. It is equal to the product of the speed at half the stopwatch.2

Before the advent of radar to determine the distance to objects in the Solar system using the method of the horizontal parallax. The error of this method is kilometer, and the measurement error of the distance using the radar centimeter.

3

The essence of the definition of the distances to the planets by the method of the horizontal parallax is to change the direction of the object when moving the observation point (parallax) – as a base is taken maximally spaced points together: the radius of the Earth. That is, the determination of distances to

**the planets**by the method of the horizontal parallax is a simple trigonometric problem. If you know all the data.4

Multiply 1 radian (the angle formed by the arc length is equal to radius expressed in seconds (206265) on the radius of the Earth (6370 km) and divide by the amount of parallax

**of the planet**at this time. The resulting value**is the distance**to**the planet**in astronomical units.5

At an annual or trigonometric parallax (base is the semimajor axis of earth's orbit) calculate distances to very distant planets and stars. By the way, parallax equal to one second determines

**the distance of**one parsec, and 1 PS = 206265 astronomical units. Divide 206265 seconds (1 radians) on the value of trigonometric parallax. The resulting quotient is**the distance of**to the interest**of the planet**.6

Finally,

**distance**to planets can be calculated using the third law of Kepler. The calculation is quite complicated, so let's proceed to the final part.Construct the squared value of the orbital period**of the planet**around the Sun. Calculate the cube root of this value. The resulting number is**the distance**from the interest**of the planet**to the Sun in astronomical units, or heliocentric**distance**. Knowing the heliocentric**distance**and the position of the planets (angular**distance****of the planet**from the Sun), you can easily calculate the geocentric**distance**.# Advice 4 : How to determine the momentum of the body

The momentum of the body is otherwise called the amount of traffic. It is determined by the product of mass and velocity. It can also be found through the duration of the force on the body. The physical meaning is not the impetus to change.

You will need

- — scales;
- speedometer or the radar;
- — dynamometer;
- calculator.

Instruction

1

Determine the mass

**of a body**with weights in kilograms. Measure its speed. Do this with the speedometer or special radar in meters per second. Calculate the momentum**of the body**p as the product of its mass m to the velocity v (p=m∙v). For example, if the speed**of the body**is 5 m/s and its mass is 2 kg, the momentum is p=2∙5=10 kg∙m/s.2

More important is the ability to find the change in momentum

**of the body**, since momentum is a characteristic of the impact in which this value is changed. To find the change in momentum**of the body**, subtract the final momentum from the initial, considering that the magnitude of this vector. Thus, the change in the momentum of bodies is equal to the vector Δp, which is the difference vector p2 (final momentum) and p1 (the initial impulse).3

If the body does not change direction, in order to find the variation of the pulse, subtract from the finite speed of primary and multiply it to the mass

**of the body**. For example, if the vehicle is moving in a straight line, the rate increased from 20 to 25 m/s, and its mass is 1200 kg, but the change in its momentum will be Δp=1200∙(25-20)=6000 kg∙m/s. If the speed**of the body**decreases, then the change in its momentum will be negative.4

If the body changes direction, looking for the difference between the vectors p2 and p1 using the theorem of the cosines or other relations.

5

Example. A ball of mass 500 g is elastically struck a smooth wall at an angle of 60º to the vertical, and his speed was 3 m/s, find the change in its momentum. Since the collision is elastic, the ball will fly away from a smooth wall is also angled at 60º, with the same velocity, 3 m/s to translate the difference in the amount, multiply the vector by -1 p1. Get that Δp is equal to the sum of vectors p2 and –p1. Applying the triangle rule, calculate Δp=√((0,5∙3)2+ (0,5∙3)2-2∙(0,5∙3)∙(0,5∙3)∙cos(60º))=0,5∙3=1.5 kg∙m/s. it is Noteworthy that the module start and end of a pulse in this case is also 1.5 kg∙m/s.

6

If we know the force acting on the body, which is the reason for changing its speed and duration of its action, then calculate the change of momentum as the product of force F on its duration Δt (Δp=F∙Δt). The power measure dynamometer. For example, if the player hit the ball with a force of 400 N, and the time of impact is equal to 0.2 s, the change in momentum of the ball will be Δp=400∙0,2=8000 kg∙m/s.