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Gravitational Constant Physics Gravitation Physics Class 11th

The satellites revolve around a planet in coplanar circular orbits in anticlockwise direction. Their period of revolutions are 1 hour and 8 hour respectively. The radius of the orbit of nearer satellite is 2 × 10³ km. The angular speed of the farther satellite as observed from the nearer satellite at the instant when both the satellites are closest is $\frac{π}{x} r a d h^{- 1}$ where x is__________.

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alok kumar singh | Contributor-Level 10

2 months ago

For A satellite T₁ = 1hour

$S o ω_{1} = 2 π r e d / h o u r$

for B satellite T₂ = 8 hour

given R₁ = 2 × 10³ Km

Relative $ω = \frac{V_{1} - V_{2}}{R_{2} - R_{1}} = \frac{2 π \times 1 0^{3}}{6 \times 1 0^{3}}$

$\Rightarrow \frac{π}{3}$ rad/hour

x = 3

For A satellite T1 = 1hour <math> <mrow> <mi>S</mi> <mi>o</mi> <mtext> </mtext> <mtext> </mtext> <msub> <mrow> <mi>ω</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mi>e</mi> <mi>d</mi> <mo>/</mo> <mi>h</mi> <mi>o</mi> <mi>u</mi> <mi>r</mi> </mrow> </math>              <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1816003047"> </o:OLEObject></xml><! [endif]-> for B satellite T2 = 8 hourgiven R1 = 2 × 103 KmRelative  <math> <mrow> <mi>ω</mi> <mo>=</mo> <mfrac> <mrow> <msub> <mrow> <mi>V</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mrow> <mi>V</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <msub> <mrow> <mi>R</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mrow> <mi>R</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>3</mn> </mrow> </msup> </mrow> <mrow> <mn>6</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </math> <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1816003048"> </o:OLEObject></xml><! [endif]->  <math> <mrow> <mo>⇒</mo> <mfrac> <mrow> <mi>π</mi> </mrow> <mrow> <mn>3</mn> </mrow> </mfrac> </mrow> </math> <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1027" DrawAspect="Content" ObjectID="_1816003049"> </o:OLEObject></xml><! [endif]->rad/hour x = 3<div><div><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1754477142phpKQEhd4.jpeg" alt="" width="217" height="181" loading="lazy"></picture></div></div>

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