Advertisements
Advertisements
प्रश्न
A Saturn year is 29.5 times the earth year. How far is the Saturn from the sun if the earth is 1.50 ×108 km away from the sun?
Advertisements
उत्तर १
Distance of the Earth from the Sun, re = 1.5 × 108 km = 1.5 × 1011 m
Time period of the Earth = Te
Time period of Saturn, Ts = 29. 5 Te
Distance of Saturn from the Sun = rs
From Kepler’s third law of planetary motion, we have
T = `((4pi^2r^3)/"GM")^(1/2)`
For Saturn and Sun, we can write
`(r_s^3)/(r_e^3) = (T_s^2)/(T_e^2)`
`r_s = r_e (T_s/T_e)^(2/3)`
`=1.5 xx 10^11 ((29.5T_e)/T_e)^(2/3)`
`=1.5 xx 10^11 (29.5)^(2/3)`
`= 1.5 xx 10^11xx 9.55`
`=14.32 xx 10^11` m
Hence, the distance between Saturn and the Sun is `1.43 xx 10^(12)` m.
उत्तर २
We know that `T^2 oo R^3`
`:.(T_s^2)/(T_e^2) = (R_s^3)/(R_e^3)`
where subscript s and e refer to the Saturn and Earth respectively.
Now `T_s/T_e = 29.5`[given]; `R_e = 1.50 xx 10^8` km
`(R_s/R_e)^3 = (T_s/T_e)`
`R_s = R_exx [(29.5)^2]^(1/3)`
`= 1.50 xx 10^8 xx (870.25)^"1.3" `km
`= 1.43 xx 10^9 km = 1.43 xx 10^12` m
∴Distance of saturn from Sum `= 1.43 xx 10^(12)` m
संबंधित प्रश्न
Let us assume that our galaxy consists of 2.5 × 1011 stars each of one solar mass. How long will a star at a distance of 50,000 ly from the galactic centre take to complete one revolution? Take the diameter of the Milky Way to be 105 ly
State Kepler's laws of planetary motion.
Answer the following question in detail.
State Kepler’s three laws of planetary motion.
The orbit of a planet revolving around a star is _______.
The square of its period of revolution around the sun is directly proportional to the _______ of the mean distance of a planet from the sun.
The mass and radius of earth is 'Me' and 'Re' respectively and that of moon is 'Mm' and 'Rm' respectively. The distance between the centre of the earth and that of moon is 'D'. The minimum speed required for a body (mass 'm') to project from a point midway between their centres to escape to infinity is ______.
The earth moves around the sun in an elliptical orbit as shown in the figure. The ratio, `"OA"/"OB"` = x. The ratio of the speed of the earth at Band at A is ______.
In our solar system, the inter-planetary region has chunks of matter (much smaller in size compared to planets) called asteroids. They ______.
Draw areal velocity versus time graph for mars.
A star like the sun has several bodies moving around it at different distances. Consider that all of them are moving in circular orbits. Let r be the distance of the body from the centre of the star and let its linear velocity be v, angular velocity ω, kinetic energy K, gravitational potential energy U, total energy E and angular momentum l. As the radius r of the orbit increases, determine which of the above quantities increase and which ones decrease.
Earth’s orbit is an ellipse with eccentricity 0.0167. Thus, earth’s distance from the sun and speed as it moves around the sun varies from day to day. This means that the length of the solar day is not constant through the year. Assume that earth’s spin axis is normal to its orbital plane and find out the length of the shortest and the longest day. A day should be taken from noon to noon. Does this explain variation of length of the day during the year?
The maximum and minimum distances of a comet from the Sun are 1.6 × 1012 m and 8.0 × 1010 m respectively. If the speed of the comet at the nearest point is 6 × 104 ms-1, the speed at the farthest point is ______.
A planet revolving in an elliptical orbit has:
- a constant velocity of revolution.
- has the least velocity when it is nearest to the sun.
- its areal velocity is directly proportional to its velocity.
- areal velocity is inversely proportional to its velocity.
- to follow a trajectory such that the areal velocity is constant.
Choose the correct answer from the options given below:
Two planets A and B of equal mass are having their period of revolutions TA and TB such that TA = 2TB. These planets are revolving in the circular orbits of radii rA and rB respectively. Which out of the following would be the correct relationship of their orbits?
How can an ellipse be drawn using pins and thread?
What is at one focus of the elliptical orbit of a planet?
The time taken by a planet to orbit the Sun depends on
