Question

A satellite is in elliptical orbit with a period of 8.00 x l-0a s about a planet of mass 7.00 x t024 kg. At aphelion, at radius 4.5 x 1-07 m, the satellite's angular speed is 7.L58 x 10-s rad/s. What is its angular speed at perihelion

Answer 1

Given that the satelite's angular speed is given,The angular speed at the perihelion is : 9.2426 * 10⁻⁵ rad/s

Given data:

Satellite period = 8 * 10⁴ s

mass of planet (Wa)  = 7 * 10²⁴ kg

Radius of Aphelion ( Ra ) = 4.5 * 10⁷ m

satellite angular speed ( Vp )= 7.158 * 10⁻⁵ rad/s

Determine the angular speed at the perihelion

Applying kepler's law

VpRp = VaRa

where:

Vp = ( Ra / Rp ) Va

and

Wp = Vp / Rp  = ( RA / Rp )² Wa  ---- ( 1 )

Note : Assuming a is distance from the center oto the end of the satelite

Rp = 2a - Ra  ---- ( 2 )

Next step : determine the value of a

applying the formula below

a = $(\frac{T\sqrt{Gmplanet} }{2\pi } )^{2/3}$ --- ( 3 )

where ; T = 8 * 10⁴ s,  G = 6.67 * 10⁻¹¹ ,  Mplanet = 7 * 10²⁴ kg

input values into ( 3 )

a = 42300747.03 m

Final step : determine the angula speed at perihelion

Back to equation ( 1 ) and ( 2 )

Wp = ( RA / 2a - Ra  )² Wa  

      = 9.2426 * 10⁻⁵ rad/s.

Hence we can conclude that Given that the satelite's angular speed is given,The angular speed at the perihelion is : 9.2426 * 10⁻⁵ rad/s

Learn more about Angular speed ; https://brainly.com/question/6860269