Gravitation

Step 1: Escape velocity from Earth
The escape velocity from the Earth's surface is given by:
v‌escape ‌=√‌

2GM

R

Here, G is the gravitational constant, M is Earth's mass, and R is Earth's radius.
Step 2: Orbital velocity at height h=R
The orbital velocity for a satellite at a distance r from the center of the Earth is:
v‌orbit ‌=√‌

GM

r

If the satellite is at a height equal to the Earth's radius ( h=R ), the total distance from Earth's center is r=R+R=2R.
So, the orbital velocity becomes:
v‌orbit ‌=√‌

GM

2R

Step 3: Find the relationship between escape velocity and orbital velocity
Let's compare the orbital and escape velocities:
‌

v‌orbit ‌

v‌escape ‌

=‌

√ GM 2R

√‌ 2GM R

Simplifying this gives:
‌

v‌orbit ‌

v‌escape ‌

=‌

1

2

Step 4: Calculate the final answer
This means the orbital velocity is half the escape velocity. Given that the escape velocity is 11.2kms−1 :
v‌orbit ‌=‌

11.2

2

=5.6kms−1