SOLAR SYSTEM

UNIVERSE

SATELLITESICY BODIES

Question [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
Calculate the escape velocity of a satellite in an orbit 300 km above Earth’s surface. Given G = 6.67 x 10^-11 N m^2 kg^-2, radius of earth is 6370 km and mass of the earth is 5.97 x 10^24 kg.
A
7.73 km s^-1
B
10.9 km s^-1
C
36.4 km s^-1
D
244 km s^-1
Explanation: 

Detailed explanation-1: -To stay in orbit, a satellite has to travel at a very high velocity, which depends on the height. So, typically, for a circular orbit at a height of 300 km above the Earth’s surface, a speed of 7.8 km/s (28, 000 km/h) is needed. At this speed, the satellite will complete one orbit around the Earth in 90 minutes.

Detailed explanation-2: -On earth, the escape velocity is around 40, 270 kmph, which is around 11, 186 m/s.

Detailed explanation-3: -The escape velocity vesc is expressed as vesc = Square root of√2GMr, where G is the gravitational constant, M is the mass of the attracting mass, and r is the distance from the centre of that mass.

Detailed explanation-4: -The escape velocity is a multiplicative factor greater than the orbital velocity: v = sqrt(2GM/r) (escape velocity = sqrt(2) * orbital velocity) If an object achieves escape velocity, it leaves its orbit and is no longer gravitationally bound to the object it was orbiting.

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