Advertisements
Advertisements
Question
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
Solution 1
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.
Solution 2
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
APPEARS IN
RELATED QUESTIONS
A comet orbits the Sun in a highly elliptical orbit. Does the comet have a constant (a) linear speed, (b) angular speed, (c) angular momentum, (d) kinetic energy, (e) potential energy, (f) total energy throughout its orbit? Neglect any mass loss of the comet when it comes very close to the Sun.
Identify the law shown in the figure and state three respective laws.
Answer the following question.
State Kepler’s law of equal areas.
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.
Observe the given figure and answer these following questions.
- What is the conclusion about the orbit of a planet?
- What is the relation between velocity of planet and distance from sun?
- ASB, CSD and ESF relation between areas explain.
State Kepler’s laws.
To verify Kepler's third law graphically four students plotted graphs. Student A plotted a graph of T (period of revolution of planets) versus r (average distance of planets from the sun) and found the plot is straight line with slope 1.85. Student B plotted a graph of T2 v/s r3 and found the plot is straight line with slope 1.39 and negative Y-intercept. Student C plotted graph of log T v/s log r and found the plot is straight line with slope 1.5. Student D plotted graph of log T v/s log r and found the plot is straight line with slope 0.67 and with negative X-intercept. The correct graph is of student
A planet revolves in an elliptical orbit around the sun. The semi-major and minor axes are a and b, then the time period is given by:
In our solar system, the inter-planetary region has chunks of matter (much smaller in size compared to planets) called asteroids. They ______.
Give one example each of central force and non-central force.
Draw areal velocity versus time graph for mars.
What is the direction of areal velocity of the earth around the sun?
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?
Halley's Comet revolves around the sun for a time period of 76 years. The aphelion distance if perihelion is given by 8.9 × 1010 m, will be ______.
(Take, the mass of sun = 2 × 1030 kg and G = 6.67 × 10-11 Nm3/kg2)
What is one practical use of Kepler’s laws?
How can an ellipse be drawn using pins and thread?
The time taken by a planet to orbit the Sun depends on ______.
Two identical particles each of mass ‘m’ go round a circle of radius a under the action of their mutual gravitational attraction. The angular speed of each particle will be ______
