Question

The orbital period of the satellite around the planet is 168 days and it's mean orbital radius is 56.35 * 10⁵ km. Calculate it's critical orbital speed.​

Answer 1

Solution : Here, a/c to question,

➜ Time period, T = 168 days

➜ Radius, r = 56.35 * 10⁵ km

Here, we know that,

➜ 1 day = 24 hour

➜ 1 day = 24 * 3600 sec

➜ 1 day = 86400 sec

➜ 1 day = 8.64 * 10⁴ sec

Hence,

➜ T = 168 days

➜ T = 168 * 8.64 * 10⁴ sec

and we know that, 1 km = 10³ m

Hence,

➜ r = 56.35 * 10⁵ km

➜ r = 56.35 * 10³ * 10⁵ m

➜ r = 56.35* 10⁸ m

Critical orbital velocity : The critical velocity of a satellite is the constant horizontal velocity given to keep the satellite in a stable circular orbit.

Now, by formula of critical velocity;

➜ v(critical) = 2πr/T

➜ v(critical) = {2 * (22/7) * 56.35 * 10⁸}/{168 * 8.64 * 10⁴}

➜ v(critical) = {(2 * 22/7) * 56.35 * 10⁸}/{1451.52 * 10⁴}

➜ v(critical) = {44/7 * 56.35 * 10⁸}/{1451.52 * 10⁴}

➜ v(critical) = {44 * 8.05 * 10⁸}/{1451.52 * 10⁴}

➜ v(critical) = 354.2 * 10⁸/1451.52 * 10⁴

➜ v(critical) = (354.2/1451.52) * 10⁴

➜ v(critical) = 0.2440200617 * 10⁴

➜ v(critical) = 2.44 * 10³ m/s

Answer : Hence, critical speed of the satellite is 2.44 * 10³ m/s.