Step 1: Escape velocity from Earth
The escape velocity from the Earth's surface is given by:
v‌escape ‌=√‌Here,
G is the gravitational constant,
M is Earth's mass, and
R is Earth's radius.
Step 2: Orbital velocity at height
h=RThe orbital velocity for a satellite at a distance
r from the center of the Earth is:
v‌orbit ‌=√‌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 ‌=√‌Step 3: Find the relationship between escape velocity and orbital velocity
Let's compare the orbital and escape velocities:
‌| v‌orbit ‌ |
| v‌escape ‌ |
=‌Simplifying this gives:
‌| v‌orbit ‌ |
| v‌escape ‌ |
=‌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 ‌=‌=5.6kms−1
