The Theoretical Time to Reach Outer Space Driving a Car
Traveling to outer space by driving a car might seem like a fun theoretical idea, but let's explore the challenges and calculations involved. The Karman line, the internationally recognized boundary of space, begins at an altitude of 100 kilometers (62 miles) above the Earth's surface. In this article, we will explore how long it would take to reach the Karman line with a car, considering both theoretical and practical scenarios.
Theoretical Calculations
The first step is to define the boundary of outer space. The Kármán line, located at an altitude of 100 kilometers, is commonly accepted as the edge of space. Next, we need to consider the average speed of a car. For this calculation, we'll use a typical highway speed of about 100 kilometers per hour (approximately 62 miles per hour).
The formula to calculate time is:
Time Distance / Speed
Substituting the values:
Time 100 km / 100 km/h 1 hour
Therefore, if you could drive your car straight up at 100 kilometers per hour, it would theoretically take you about 1 hour to reach the Karman line. However, this is purely a theoretical scenario, as cars are not designed to operate in the extreme conditions of outer space!
No Air Resistance: A Cheeky Hypothetical
If we presume that there is no air resistance and no air, the Karman line is just the starting point for outer space. In this case, you would already be in space right at the altitude of the Karman line. But let's get more precise with the commonly accepted definition.
Practical Scenario: Falcon 9 Rocket
For a more practical approach, let's consider a spacecraft like the Falcon 9 rocket. The Karman line is defined as 100 km above the ground. A spacecraft's acceleration is affected by its weight and thrust. In our scenario, we will assume the Falcon 9, with a modified vacuum configuration for all engines, is flying straight up into the atmosphere. Let's delve into the detailed calculations.
Initial Acceleration and Thrust
The Falcon 9 stage 1 uses nine Merlin 1D engines, each with a thrust of 981 kN. The total thrust of the first stage is 8.829 MN. The ship has a wet mass (full fuel load) of about 544,600 kg. At launch, the thrust-to-weight ratio is about 1.65, giving an initial excess acceleration of 0.65 G's, or 6.4 m/s^2.
Effects of Mass and Thrust
Stage 1 burns for 162 seconds, during which the mass decreases. The dry mass of stage 1 is 22,200 kg, and the wet mass of stage 2 is 111,500 kg. At the end of the first stage burn, the remaining mass is approximately 133,700 kg, but the thrust remains constant. The thrust-to-weight ratio increases, reaching 6.73. This results in a new excess acceleration of 5.73 G's, or 56.2 m/s^2.
Accurate Time Calculation
Using calculus, the equation for position with respect to time needs to be determined. This involves integrating the third derivative of the acceleration equation. After performing the necessary integrals, we find the time required to reach 100 km (rising straight up). The result is approximately 107.28 seconds.
Therefore, in a Falcon 9 tailored for the job, it takes about 107.28 seconds to reach the Karman line under optimal conditions without air resistance.
These calculations highlight the practical challenges of reaching space, emphasizing the importance of specialized spacecraft designed for the unique conditions of outer space.