Astro 001 Unit 1; Gravity
Newton's Second Law:
The acceleration of a body due to a force will be in the same direction as the force, with a magnitude directly proportional to its mass. (This is usually written as F = ma, or Force = mass x acceleration).
Second Law
The acceleration of a body due to a force will be in the same direction as the force, with a magnitude dirtily proportional to its mass (F = m A) (F = ma, or Force = mass X acceleration)
If the mass is .25m as high, you jump..
4 times as high
Radius 2x that of Earth, how high?
4 times as high
The Earth radius is about 6400 km. If you were in orbit in the Space Station 150 km above the ground, the force gravity you feel from Earth would be:
Slightly weaker than when you are standing on Earth
Mars has lower surface gravity than Earth?
TRUE *Mars has about 1/10 the mass of the Earth and about 1/2 the radius of Earth
The force of gravity by the Sun keeps the planets in orbit around it, but how do the planets affect the Sun?
They exert an equally strong pull on the Sun, causing it to move slightly.
Inertia
-Newton's First Law -The tendency of an object at rest to remain at rest, or of a moving object to continue moving. -When one applies a force to an object, it causes the object to accelerate (the Second Law), which may be a deceleration (negative acceleration) depending on the direction in which the force is applied. -In addition to causing acceleration (positive or negative), an applied force may alter the direction of motion of the target object.
Saturn has about 100x
...
The moon has about 1/100 the mass of Earth and about 1/4 the radius. What is the surface gravity of the Moon compared to Earth?
16% of the gravity of Earth
Radius 3x as Earth, how high?
9 times as high
According to Newton's Second Law of Motion, if the net force acting on the object increase what the mass of the object remains constant, what happens to the acceleration?
Acceleration Increases
Newton's Laws of Universal Gravitation
All objects with mass experience attraction towards each other as a result of the gravitational force between them. The strength of this force between two objects is given by
Newton's First Law:
An object at rest, or in motion in a straight line at a constant speed, will remain in that state unless acted upon by a force.
If you were to sit on the ground, there would be a force due to gravity pulling you toward the Earth. Which is true according to Newton's 3rd law? A. You are pulling the Earth toward yourself with the same force. B. You are not exerting any force on the Earth. C. You are pushing the Earth away from yourself with the same force. D. You will continue to sit in the same place without moving.
C. You are pushing the Earth away from yourself with the same force.
As the mass of the planet increases, the jump height...by the same factor as mass
Decreases *Increasing the mass decreases the jump height. Mass of a planet and jump height are inversely related.
Jupiter has about 300x the mass of Earth and about 10x the radius. What is the surface gravity of Jupiter compared to Earth?
Despite being over 300x as massive as Earth, Jupiter has only 3x the surface gravity.
G (m1 m2) Fg = ————————— r2
Fg is the force of gravity G is the universal constant of gravitation m1 is the mass of one object m2 is the mass of a second object r is the distance between the two objects
Newton's Third Law
For every action, there is an equal and opposite reaction
Newton's Third Law:
For every action, there is an equal and opposite reaction.
FORMULA
G (Mars) = Mass of MARS/ Radius of MARS squared = (Mass of earth) / (Radius of earth/2) squared = 4/10 gravity of Earth
How high are you jumping at twice Earth's mass compared to Earth's mass?
Half as high
As the radius increases, the jump height.... as the square of the radius
Increases *Gravity is inversely proportional to the square of the radius
If the Earth were moved to half its current distance from the Sun, how would the force of gravity by the Sun on the Earth change?
It would become four times stronger
What would happen to the Earth if the Sun's gravity somehow "turned off" instantaneously?
It would continue to move in a line in the same direction it was moving when the gravity turned off.
Keep mass at Earth's mass but change the radius to half the radius of Earth..how much higher do you jump?
One quarter as high *same mass, smaller radius, jump less
What did Newton's Law of Universal Gravitation tell us about how gravity works?
The force of gravity from the Sun will be stronger on an object with more mass
Gravitational Force
The gravitational force is then directly proportional to the mass of each interacting object (or to the product of them), and inversely proportional to the distance between them, squared.
When the mass is .5m as high you jump...
Twice as high
Since the jump height is half as high what does that tell us about gravity?
Twice as much
F = m a
where 'a' is the acceleration; if the force 'F' is due to gravity, the 'a' may be written as 'g' ( F = m g )