A satellite is in elliptical orbit with a period of 7.20 104 s about a planet of mass 7.00 1024 kg. At aphelion, at radius 5.1 107 m, the satellite's angular speed is 4.987 10-5 rad/s. What is its angular speed at perihelion?

1.64xrad/s

Explanation:

Given:

satellite is in elliptical orbit with a period T= 7.20 x s

Mass of planet m=  7.00x kg

Satellite's angular speed ωa- = 4.987 10-5 rad/s

At aphelion, at radius Ra= 5.1 x 10^7 m

Assuming torque is zero for this system, therefore, the conservation of angular momentum can be defines as

Lp = La

Ip ωp = Ia ωa--->eq(1)

Where,

'a' represents aphelion and 'p' represents perihelion

ω represents  angular velocity

and I represents the rotational inertia

Since, I= 1/2 mR²

Here R is the radius at  aphelion /  perihelion

m = mass of planet

eq(1)=> ωp= Ia ωa/ Ip

ωp= (1/2 m Ra² ωa) / 1/2 m Rp²

ωp= (Ra/Rp)² ωa --->eq(2)

In order to find Rp, we use : 2a= Rp + Ra

where a represents semimajor axis

with the help of Kepler's third law for elliptical orbits

a= ∛(GmT²/4π²)

a= ∛ 6.67x x 7.00x x (7.20 x )² / 4π²

a=  3.97 x m

2a= Rp + Ra

Rp= 2a-Ra

Rp= 2 x 3.97 x -  5.1x

Rp= 2.84 x m

Substituting all the required values in eq 2, we have

ωp= (Ra/Rp)² ωa

ωp= (5.1x /2.84 x )² x  4.987 x

ωp= 3.224 x 4.987 x

ωp= 1.64xrad/s

Therefore, angular speed at perihelion is 1.64xrad/s

E = 124.7 N / C

Explanation:

Let's analyze the exercise: the microwave creates an electromagnetic wave of frequency F = 2.45 GHz, this wave is introduced into the microwave cavity and is reflected on the metal walls, which is why one or more standing waves are formed.

The electric field of the standing wave is

            I = E²

            E =√I

where I is the intensity of the radiation.

What is it

             I = P / A

where P is the effective emission power, almost all the power of the microwave and A is the area of ​​the cavity, in the most used microwaves

P = 700 W and the area is A = 25 x 18 cm² = 0.045 m²

             I = 700 / 0.045

             I = 15555.56 W/m²

let's calculate the electric field

            E = √15555.56

            E = 124.7 N / C