Distance of a heavenly body in the Solar system
The distance of a planet can be accurately measured by the radar echo method. In this method, the radio signals are sent towards the planet from a radar. These signals are reflected back from the surface of a planet. The reflected signals or pulses are received and detected on Earth. The time t taken by the signal in going to the planet and coming back to Earth is noted. The signal travels with the velocity of the light c. The distance s of the planet from the Earth is given by s = ct/2.
Size of a planet
It is possible to determine the size of any planet once we know the distance S of the planet. The image of every heavenly body is a disc when viewed through a optical telescope. The angle θ between two extreme points A and B on the disc with respect to a certain point on the Earth is determined with the help of a telescope. The angle θ is called the angular diameter of the planet. The linear diameter d of the planet is then given by
d = distance × angular diameter
d = s × θ
Surface temperatures of the planets
The planets do not emit light of their own. They reflect the Sun's light that falls on them. Only a fraction of the solar radiation is absorbed and it heats up the surface of the planet. Then it radiates energy. We can determine the surface temperature T of the planet using Stefan's law of radiation E = σ T4 where σ is the Stefan's constant and E is the radiant energy emitted by unit area in unit time.
In general, the temperature of the planets decreases as we go away from the Sun, since the planets receive less and less solar energy according to inverse square law. Hence, the planets farther away from the Sun will be colder than those closer to it. Day temperature of Mercury is maximum (340oC) since it is a planet closest to the Sun and that of Pluto is minimum (−240oC). However Venus is an exception as it has very thick atmosphere of carbon−di−oxide. This acts as a blanket and keeps its surface hot. Thus the temperature of Venus is comparatively large of the order of 480oC.
Mass of the planets and the Sun
In the universe one heavenly body revolves around another massive heavenly body. (The Earth revolves around the Sun and the moon revolves around the Earth). The centripetal force required by the lighter body to revolve around the heavier body is provided by the gravitational force of attraction between the two. For an orbit of given radius, the mass of the heavier body determines the speed with which the lighter body must revolve around it. Thus, if the period of revolution of the lighter body is known, the mass of the heavier body can be determined. For example, in the case of Sun − planet system, the mass of the Sun M can be calculated if the distance of the Sun from the Earth r, the period of revolution of the Earth around the Sun T and the gravitational constant
G are known using the relation M = 4π r3 / GT2
The ratio of the amount of solar energy reflected by the planet to that incident on it is known as albedo. From the knowledge of albedo, we get information about the existence of atmosphere in the planets. The albedo of Venus is 0.85. It reflects 85% of the incident light, the highest among the nine planets. It is supposed to be covered with thick layer of atmosphere. The planets Earth, Jupiter, Saturn, Uranus and Neptune have high albedoes, which indicate that they possess atmosphere. The planet Mercury and the moon reflect only 6% of the sunlight. It indicates that they have no atmosphere, which is also confirmed by recent space probes.
There are two factors which determine whether the planets have atmosphere or not. They are (i) acceleration due to gravity on its surface and (ii) the surface temperature of the planet.
The value of g for moon is very small (¼th of the Earth). Consequently the escape speed for moon is very small. As the average velocity of the atmospheric air molecules at the surface temperature of the moon is greater than the escape speed, the air molecules escape.
Mercury has a larger value of g than moon. Yet there is no atmosphere on it. It is because, Mercury is very close to the Sun and hence its temperature is high. So the mean velocity of the gas molecules is very high. Hence the molecules overcome the gravitational attraction and escape.
Conditions for life on any planet
The following conditions must hold for plant life and animal life to exist on any planet.
1. The planet must have a suitable living temperature range.
2. The planet must have a sufficient and right kind of atmosphere.
3. The planet must have considerable amount of water on its surface.
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