Question 165: Gravitation

Question

Two satellites A and B of masses 200 kg and 400 kg are revolving round the earth at height of 600 km and 1600 km respectively.
If T
A
and T
B
are the time periods of A and B respectively then the value of T
B
$$-$$ T
A
:
[Given : radius of earth = 6400 km, mass of earth = 6 $$	imes$$ 10
24
kg]

Accepted Answer

$$T = 2\pi \sqrt {{{{r^3}} \over {GM}}} $$
$${T_A} = 2\pi \sqrt {{{{{\left( {6400 + 600} ight)}^3}} \over {GM}}} $$
$${T_A} = 2\pi  	imes {10^9}\sqrt {{{{7^3}} \over {GM}}} $$
$${T_B} = 2\pi  	imes {10^9}\sqrt {{{{8^3}} \over {GM}}} $$
$${T_B} - {T_A} = {{2\pi {{10}^9}} \over {\sqrt {GM} }}\left[ {8\sqrt 8  - 7\sqrt 7 } ight]$$
$$ = 314 	imes 4.107$$
$$ = 1289.64$$
$$ = 1.289 	imes {10^3}s$$

Answer

1.33 $$	imes$$ 10
3
s

Answer

4.24 $$	imes$$ 10
2
s

Answer

3.33 $$	imes$$ 10
2
s

Answer

4.24 $$	imes$$ 10
3
s

Gravitation

Two satellites A and B of masses 200 kg and 400 kg are revolving round the earth at height of 600 km and 1600 km respectively. If T A and T B are the time periods of A and B respectively then the value of T B $- T A : [Given : radius of earth = 6400 km, mass of earth = 6 \times$ 10 24 kg]

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