The cosmic speed and orbital speed we discussed are all in a vacuum, which is the final flight state of a satellite without thrust.
The first cosmic speed
The first cosmic speed is the minimum speed needed for an object to escape the gravitational pull of a planet. For Earth, the first cosmic speed is about 7.93 kilometers per second. This means that if an object is traveling at or above this speed, it will escape Earth's gravity and continue traveling through space. If an object is traveling below this speed, it will eventually fall back to Earth.
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| Earth, Satellite, orbit and velocity |
Here is how we calculate the first cosmic speed:
Where:
- R is the radius of the Earth, which is equal to 6.37 × 10^6 m (r = R+h)
- G is the gravitational constant, which is equal to 6.67 × 10^-11 N m^2 / kg^2
- M is the mass of the Earth, which is equal to 5.97 × 10^24 kg
- m is the mass of satellite
The first cosmic speed is the minimum speed needed to launch a satellite into orbit. It is also the maximum speed a satellite can travel while in orbit. To get into space, a satellite must reach the first cosmic speed at launch.
Orbital speed
Satellite orbit speed is the speed at which a satellite must travel in order to maintain its orbit around a planet. The orbital speed of a satellite depends on the mass of the planet and the distance between the satellite and the planet.
where:
- v is the orbital speed in meters per second
- G is the gravitational constant (6.673 x 10^-11 m^3 kg^-1 s^-2)
- M is the mass of the planet in kilograms
- r is the distance between the center of the planet and the center of the satellite in meters
From the speed equation, we can tell that objects in higher orbits travel at slower speeds.
Orbital speed in orange color is slower
For example, Geostationary satellites orbit the Earth at an altitude of 35,786 kilometers (22,236 miles). At this altitude, they have to travel at a speed of 3.07 kilometers per second (1.91 miles per second) in order to maintain their orbit.
Can we launch a satellite with speed of 1m/S and send it into space?
Yes, it is theoretically possible to launch a satellite with a speed of 1m/s. However, this is not feasible in practice because we cannot carry unlimited fuel.
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| Tsiolkovsky rocket equation |
This is Tsiolkovsky rocket equation. It is a fundamental equation in rocketry. It is used to design rockets and to calculate the performance of rockets. The equation is also used to calculate the amount of fuel that is needed to reach a certain destination in space.Where:
- Vm is the change in velocity of the rocket
- v_r is the effective exhaust velocity of the rocket
- m_max is the initial mass of the rocket
- m_min is the final mass of the rocket
To To achieve a certain speed, a rocket can carry more fuel, but the excess fuel becomes a deadweight, limiting the benefits of carrying excess fuel.
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| Vm v.s ratio of m_max/m_min |
Multi-stage rockets are designed to use fuel more efficiently and improve mass ratio. This reduces the mass of the rocket, which allows the remaining stages to accelerate the rocket to a higher velocity.
Imagine there is a mountain with a platform at the top. You need to climb to the top of the mountain. What would you like to do once you reach the top? Usually, When riding a bike up a low hill, you can usually build up speed and maintain it until you reach the platform at the top.
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| Build up speed and maintain it until you reach the top |
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Space