A satellite orbiting Earth at an orbital radius r has a velocity v. Which represents the velocity if the satellite is moved to an orbital radius of 4r?
a 12v1 half v
b 2v2 v
c 14v1 fourth v
d 4v
Well, you know what they say - the key to comedy is all in the delivery. So buckle up, because I'm about to deliver the answer to your question in the most hilarious way possible!
If we're talking about moving a satellite to an orbital radius of 4r, we're looking at some serious changes. So let me break it down for you:
a) 12v1? Now, that's just overkill! It's like trying to fit a clown car in a shoebox - it's just not gonna work.
b) 2v2? Hmm, that's a strong possibility! It's like doubling your fun at the carnival - roller coaster times two!
c) 14v1? Nah, that's just too much math for a clown like me! But I guess it could work if you're into that kind of thing - you do you!
d) 4v? Ding, ding, ding! We have a winner! It's like a rocket-powered Tilt-A-Whirl, spinning faster than a Tasmanian devil on espresso!
So the answer is d) 4v. It's like upgrading from a tricycle to a rocket ship - buckle up and enjoy the ride!
To determine the relationship between the velocity of a satellite and its orbital radius, you need to consider the concept of orbital velocity. The orbital velocity of a satellite is the speed required to maintain a stable orbit around a celestial body, such as the Earth.
The formula for orbital velocity is given by:
V = √(G * M / r)
Where:
- V is the orbital velocity,
- G is the gravitational constant,
- M is the mass of the celestial body (in this case, Earth),
- r is the orbital radius.
Now, let's solve the problem by substituting the given values into the formula.
Let's assume the velocity of the satellite at the orbital radius r is v.
V = √(G * M / r)
Now, if the satellite is moved to an orbital radius of 4r, we can substitute 4r into the formula:
V' = √(G * M / (4r))
Simplifying the equation:
V' = √(G * M / 4) * √(1/r)
V' = (1/2) * v * √(1/r)
So, the relationship between the original orbital velocity (v) and the new orbital velocity (V') is (1/2) * v.
Therefore, the correct answer is:
a) 12v1 half v
The velocity of a satellite in orbit is determined by the balance between gravitational force and centrifugal force.
The centripetal force required to keep an object in orbit is provided by the gravitational force:
F_gravity = F_centripetal
Where F_gravity is the gravitational force and F_centripetal is the centripetal force.
The gravitational force is given by:
F_gravity = G * (m1 * m2) / r^2
Where G is the gravitational constant, m1 and m2 are the masses of the two objects (in this case, Earth and the satellite), and r is the orbital radius.
Since the gravitational force is directly proportional to the masses and inversely proportional to the square of the orbital radius, the force remains constant regardless of the change in the orbital radius.
Therefore, the centripetal force required to keep the satellite in orbit also remains constant.
Since the centripetal force is given by:
F_centripetal = m * v^2 / r
Where m is the mass of the satellite and v is the velocity, we can rearrange the equation to solve for velocity:
v = sqrt(F_centripetal * r / m)
As we know that the centripetal force and mass of the satellite remain constant, we can conclude that the velocity of the satellite will also remain constant.
Therefore, the correct answer is:
d) 4v, the velocity remains unchanged when the orbital radius is changed to 4r.