## Gravitation - Kepler's Laws Of Planetary Motion

Numerical Problems with Solutions

Question 1: The planet Neptune travels around the Sun with a period of 165 years. Show that radius of orbit is approximately 30 times that of the Earth's orbit, considering their orbits circular.

Answer:
Let T₁ = T(earth) = 1 year
T₂ = T(Neptune) = 165 years

Let R₁ and R₂ be the radii of the circular orbits the Earth and the Neptune respectively.

```   T₁²   R₁³
--- = ----
T₂²   R₂³

R₁³ × T₂²
∴ R₂³ = ----------
T₁²

R₁³ × 165²
R₂³ = ----------   = 165²R₁³
1²

R₂ ≈ 30R₁

```

Question 2: A planet of mass 'm' moves around the sun of mass M in an elliptical orbit. The maximum and minimum distance of the planet from the sun are r₁ and r₂ respectively. The time period of the planet is proportional to

(a) r₁³⸍²
(b) r₂³⸍²
(c) (r₁ + r₂)³⸍²
(d) (r₁ - r₂)³⸍²

Answer: (c) (r₁ + r₂)³⸍²

Question 3: If the distance between the earth and the sun were half its present value, the number of days in a year would have been
(a) 64.5
(b) 129
(c) 182.5
(d) 730

Answer: (b) 129

Question 4: The time period of the satellite of the earth is 5 hr. If the separation between earth and satellite is increased to 4 times the previous value, then what will be the new time period of satellite.

Answer
```  T₁²   R₁³
--- = ----
T₂²   R₂³

∴ T₂² = 64 × 25
∴ T₂  = 40 Hours
```

☛See also:
Laws Of Motion (Revision Test)

Gravitation - Understanding Mass and Weight
Gravitation - Kepler's Laws

Centre Of Mass and Rotational Motion (Assignment)  #### Post a comment

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