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ASTRO101: escape velocity
- Course
- ASTRO101 (ASTRO101)
- Institution
- University Of Alberta (UofA)
Questions on escape velocity assignment
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Before we go into orbit, let's discuss an important di erence in physics, the di erence betweenweight and mass. Mass is a property of an object that can describe as the ability for that object to
resist acceleration. Weight on the other hand depends on the local gravitational eld. Mass always
stays the same. If my mass is 75 kilograms, I'll be 75 kilograms whether I'm here on Earth on the
moon or somewhere in deep space. But weight is actually a measurement of the force felt by an
object within a gravitational eld, which means that weight can change in di erent gravities.
weight m
g
It's a product of the mass and the local gravitational eld. So weight = m times g in multiples of one
Earth gravity. On the moon where gravity is roughly one-sixth of Earth's gravity, my mass is still 75
kilograms but my weight is reduced by a factor of 6. What does it mean to be weightless if
weight depends on the local gravity? Well, imagine a region of space so far from stars and planets
that the local gravitational eld is very close to 0. What would someone with a mass of 75 kilograms
feel when there is zero gravitational force on them? They would feel a weight of zero kilograms. So
when an astronaut is oating freely in space, are they weightless? No, it's a common misconception
that astronauts experience weightlessness when they are above Earth's atmosphere where gravity
is weak. In fact, there's still enough gravity in the environment around Earth that they have a
measurable weight. However, this is di erent from experiencing free fall. Acceleration in a
gravitational eld that is not restricted by any other forces. Astronauts feel weightless, because
both the spacecraft that they're in and the astronauts themselves are in a state of free fall above the
Earth. A body is in free fall whenever gravity is the only force acting upon it.
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If I release a ball either here or from up high in space, the only force acting on the ball while it's
moving is gravity. When it's moving it's in a state of free fall and experiences weightlessness. Since
the force of gravity acts on it, the ball accelerates and moves towards the Earth until it hits the
Earth's surface. What do you think would happen when the ball is thrown horizontally?
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Newton was the rst to imagine what would happen if you climbed a tall mountain in order to re a
cannonball horizontally? Newton reason that the cannonball would curve towards the Earth due to
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, gravity. If the cannonball was red at a faster speed it would go a longer distance. And eventually if
the cannonball could be red fast enough it would fall towards the ground on a curved trajectory
that matches the curvature of Earth's surface.
This was the rst time someone had reckoned about orbital motion. This is very similar to how ying
is described in Douglas Adams A Hitchhiker's Guide to the Galaxy. Where it is stated, there's an art
to ying or rather a knack. The knack lies in learning how to throw yourself at the ground and miss.
When an astronaut orbits the Earth in the International Space Station, the only force acting on the
astronaut is gravity. The astronaut is traveling in a stable orbit around the Earth, so although gravity
is pulling on the astronaut towards the Earth the circular motion makes it possible for the astronaut
to miss the Earth.
One way to experience weightlessness without being in orbit or at a vast distance from the Earth is
to y in an airplane on a parabolic trajectory. Special aircraft that can withstand many times the
force of gravity navigate to a high-altitude before climbing into a inverted parabolic ight path.
During the arc of the parabola, the airplane and the occupants within it only experience the force of
gravity, and therefore, they feel weightless. These moments feel like zero gravity, but they only last
about 20 seconds. The airplane can't stay in free fall for very long for obvious reasons.
>> [INAUDIBLE] 12, 11, 10, 9, ignition sequence start 6, 5, 4, 3, 2, 1, 0, all engine launch. We have
a lift of [INAUDIBLE]. >> [INAUDIBLE] four forward drifting to the right a little. >> [INAUDIBLE] >>
Rockets like the Saturn V that carried the crew of the Apollo 11 mission to The moon must expend
energy to climb through Earth's gravitational eld. The speed of a spacecraft dictates how high it
will go in a given scenario. So just how much energy is required for a rocket to escape from a planet
entirely?
Let's consider an example of a rocket escaping from Earth. Kinetic energy is the energy associated
with the speed of an object, which supplied to a rocket by burning fuel and expelling it from the
rockets nozzles. The energy required to break the gravitational grasp of a planet like Earth depends
on the mass of the planet as well as its size. When a speed is associated with kinetic energy of a
departing rocket, we call it the escape velocity. Earth has an escape velocity which is roughly 11.2
kilometers per second, which is more than 40,000 kilometers per hour. But let's not get too carried
away, getting to space is much more complicated than merely getting a vehicle to the right speeds.
This calculation considers the pure physics involved in climbing out of the gravitational potential
well. So we ignore otherwise important factors like air resistance. 11.2 kilometers per second is the
instantaneous velocity you'd need traveling directly upwards from Earth's surface in order to escape
Earth's gravitational well. At sea level, 11.2 kilometers per second is equivalent to Mock 33, which is
fast enough to make the air around the spaceship into a boiling plasma. So instead rockets
accelerate out of our atmosphere starting from a standstill.
Although we used Apollo 11 to introduce you to the concept of escape velocity, it's worth pointing
out that in order to reach the moon, the astronauts never exceeded Earth's escape velocity at all.
The moon is gravitationally bound to Earth and avoids there, hasn't escaped from Earth's
gravitational sphere of in uence. The moon itself is also trapped within Earth's gravitational well.
Out of all the spacecraft launched by humanity, only a few have achieved Earth's escape velocity,
those spacecraft which traveled to other planets in our solar system. But a small subset of
spacecraft have voyaged well beyond the Earth's grasp and escaped from the gravitational pull of
the entire solar system. One such spacecraft Voyager 2 launched in 1977 and is now considered to
be an Interstellar Traveler.
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