## Planetary calculations

Planetary calculations

### Measurement of distance of heavenly bodies

Parallex Methode D = b/θ

Where D is the distance of planet from earth θ is the parallactic angle and b is called basis.

This method is suitable to study the distance of the inferior planets (i.e. those planets which are closer to sun than earth, such as Mercury and Venus) from the earth or from the sun.

r1=rsin € and r2 = r cos €

Where r1 = distance of the planate from the sun, r2 = distance of the planet from the earth,

r = distance of the sun from the earth, € = maximum value of planet’s elongation.

By using Kepler’s third law

The distance of superior planets (i.e. those planets whose orbital path is greater than of earth’s orbit around the sun) can be measured by applying kepler’s third law of planetary motion.

According to this law T^{2} ∝ R^{3} and R2=R1(T2/T1)^{2/3}

Where R1 , R2 = Semi major axis of the two planets.

T1 ,T2 = time period of revolution of two planets.

### Size of heavenly bodies

Size of heavenly bodies (D) , like moon, planet or satellite can be given by D = ra .

Where r is the distance of the heavenly bodies from the earth and a is the angle subtended by the diameter of the heavenly body at a point on the surface of earth.

### Mass of a planet

When a planet and its satellite (or moon) both resolve around a common centre of mass O, from a binary system Then

M1+M2 =4π^{2}a^{3}/T2G

Where, M1, M2 = masses of the planate and satellite

A = distance between the planate and satellite

T = common time period of revolution of the planate and satellite about the centre of mass.

G = Gravitational constant.

### Surface temperature of a planet

Using Stefan’s law, i.e. E =σ T^{4} where E is the thermal energy emitted per second per unit area of the planet and T is its surface temperature, σ is the Stefan’s constant.

Using Wien’s Displacement law

λm T=b.

Where λm is the wavelength corresponding to maximum intensity of radiation emitted from the back body at temperature T( in Kelvin) and b is the Wien’s constant.

### Existence of atmosphere on a planet

The existence of atmosphere on a planet can be decided by two factors:

1) Accelerations due to gravity

2) Surface temperature of the planet

The planet like Mercury, Mars and Pluto has large value of acceleration due to gravity but they have high temperature also. With the increase in temperature, the average velocity of the gas molecules increases and becomes more then their escape velocities. Due to this, the gas molecules have escaped one by one and there is no atmosphere.

### Basic condition for the existence of life on a planet

1) There should be suitable temperature range as required for the life to exist on a planet.

2) There should be proper atmosphere free from poisonous gases.

3) There should be plenty of water.

These conditions do not exist on any other planet except our earth. Hence the life is not possible on any other planet except earth.