Advertisements
Advertisements
Question
Assume that you are in another solar system and provided with the set of data given below consisting of the planets’ semi-major axes and time periods. Can you infer the relation connecting semi-major axis and time period?
| Planet (imaginary) | Time period (T) (in year) | Semi-major axis (a) (in AU) |
| Kurinji | 2 | 8 |
| Mullai | 3 | 18 |
| Marutham | 4 | 32 |
| Neithal | 5 | 50 |
| Paalai | 6 | 72 |
Advertisements
Solution
Time period `"T"^2 ∝ "a"^3`
T1 = 2; a1 = 8
a1 = 22 × 2 = 2T1 (T1 = 2)
a2 = 32 × 2 = `2"T"_2^2` (T2 = 3)
a3 = 42 × 2 = `2"T"_3^2` (T3 = 4)
a4 = 52 × 2 = `2"T"_4^2` (T4 = 5)
a5 = 62 × 2 = `2"T"_5^2` (T5 = 6)
∴ `"a" ∝ 2"T"^2`
APPEARS IN
RELATED QUESTIONS
Choose the correct option.
The weight of a particle at the center of the Earth is _______.
The gravitational potential due to the Earth is minimum at _______.
The linear momentum and position vector of the planet is perpendicular to each other at _________.
According to Kepler’s second law, the radial vector to a planet from the Sun sweeps out equal areas in equal intervals of time. This law is a consequence of ___________.
State Newton’s Universal law of gravitation.
Suppose unknowingly you wrote the universal gravitational constant value as G = 6.67 × 1011. instead of the correct value, G = 6.67 × 10−11, what is the acceleration due to gravity g' for this incorrect G? According to this new acceleration due to gravity, what will be your weight W'?
Four identical particles of mass M are located at the corners of a square of side 'a'. What should be their speed if each of them revolves under the influence of the other's gravitational field in a circular orbit circumscribing the square?
Which of the following statements is NOT a characteristic of gravitational force as described in the source?
Who described Earth’s rotation and orbits before Newton?
What causes tides on Earth?
