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
RELATED QUESTIONS
State Kepler's law of orbit and law of equal areas.
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
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.
Answer the following question in detail.
State Kepler’s three laws of planetary motion.
Observe the given figure and answer these following questions.
The orbit of a planet moving around the Sun
- What is the conclusion about the orbit of a planet?
- What is the relation between velocity of planet and distance from sun?
- Explain the relation between areas ASB, CSD and ESF.
Write the Kepler's laws.
If the distance between the sun and the earth is made three times, then attraction between the two will ______
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 ______.
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
Both earth and moon are subject to the gravitational force of the sun. As observed from the sun, the orbit of the moon ______.
In our solar system, the inter-planetary region has chunks of matter (much smaller in size compared to planets) called asteroids. They ______.
If the sun and the planets carried huge amounts of opposite charges ______.
- all three of Kepler’s laws would still be valid.
- only the third law will be valid.
- the second law will not change.
- the first law will still be valid.
Supposing Newton’s law of gravitation for gravitation forces F1 and F2 between two masses m1 and m2 at positions r1 and r2 read F1 = – F2 = `- r_12/r_12^3 GM_0^2 ((m_1m_2)/M_0^2)^n` where M0 is a constant of dimension of mass r12 = r1 – r2 and n is a number. in such a case.
- the acceleration due to gravity on earth will be different for different objects.
- none of the three laws of Kepler will be valid.
- only the third law will become invalid.
- for n negative, an object lighter than water will sink in water.
The centre of mass of an extended body on the surface of the earth and its centre of gravity ______.
- are always at the same point for any size of the body.
- are always at the same point only for spherical bodies.
- can never be at the same point.
- is close to each other for objects, say of sizes less than 100 m.
- both can change if the object is taken deep inside the earth.
Draw areal velocity versus time graph for mars.
Out of aphelion and perihelion, where is the speed of the earth more and why?
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 ______.
What is one practical use of Kepler’s laws?
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 ______
