What Would Happen If an Astronaut Throws a Wrench to Earth?
The scenario of an astronaut tossing a wrench into space towards Earth is an intriguing one. Various factors, including initial velocity, Earth's gravity, atmospheric drag, terminal velocity, and impact, all play significant roles in determining the trajectory and fate of the wrench. Let’s explore these factors in more detail.
Initial Velocity
Assuming an astronaut grabs a wrench and gives it a strong push towards Earth from the International Space Station (ISS), the wrench will initially move due to the astronaut's applied force. Depending on the force and angle at which the wrench is thrown, it will begin its descent towards the planet.
Earth's Gravity
As the wrench moves away from the ISS, it will encounter the gravitational pull of Earth. Gravity acts as a downward force, pulling the wrench towards the planet's surface. The strength of this pull increases as the distance between the wrench and the Earth's surface decreases, contributing to the wrench's acceleration.
Atmospheric Drag
As the wrench enters the Earth's atmosphere, it will experience significant drag. The atmosphere slows the wrench down due to friction. Depending on the height from which it is thrown, the wrench may experience extreme heat, potentially burning up due to the intense friction created during high-speed entry.
Astronaut Aroldis Chapman and His Fastball
For some context, compare this to the fastest pitch ever recorded by Aroldis Chapman of the Cincinnati Reds, at 105.1 mph (169.0 km/h). The ISS orbits the Earth at approximately 17,129 mph (27,574 km/h) in a near-circular orbit. If we consider Chapman's pitch to be thrown towards Earth at a right angle to the tangent of the ISS's speed, the following calculations can help us understand the trajectory:
Vector Addition of Velocities
The resultant velocity of the thrown wrench can be calculated using vector addition. The formula is:
Vresultant sqrt(Viss^2 Vpitch^2)
Substituting the values:
Viss 17129 mph, Vpitch 105.1 mph
Vresultant sqrt(17129^2 105.1^2) ≈ 17129.322 mph
The angle at which the wrench is thrown can be calculated as:
θ asin(105.1 / 17129.322) ≈ 0.3516 degrees (or 20.09 minutes)
This calculation indicates that the wrench would fly about 20 miles away in 21 minutes and then return in roughly the same amount of time. This scenario, despite the interesting calculations, raises concerns about potential hazards for astronauts and equipment.
Orbital Mechanics and Altitude Considerations
To shoot something back to Earth, one would need to consider orbital mechanics. An object would need to be fired in such a way that it falls from a circular orbit of 264.64 miles (425.9 km) to a vacuum perigee altitude (VPA) of 37.28 miles (60 km). This requires changing the circular orbit to an elliptical one, with an apogee of 264.64 miles (425.9 km) and a perigee of 37.28 miles (60 km).
In English units, these are approximately 264.64 miles, 37.28 miles, 4223.4 miles, and 3996 miles. The resultant speed of the object would be approximately 105.1 mph at perigee, as it serves as the point of closest approach to Earth.
Conclusion
While the wrench would start falling towards Earth, it would likely encounter significant atmospheric drag, potentially burning up. If it survives the fall, it would eventually impact the ground, which could be dangerous. Astronauts and scientists should be cautious of such scenarios to ensure the safety of both personnel and infrastructure.