Halley's Comet orbits the sun about every 75 years due to the gravitational force the sun provides. Compare the gravitational force between Halley's Comet and the sun when the Comet is at aphelion (its greatest distance from the sun) and d is about 4.5×10^12m the force at perihelion (or closest approach), where d is about 5.0×10^10m. (I really don't know where to start :( )
You're in a bit of a pickle if you don't know the mass of Halley's comet.
Fg = Gm1m2/r^2
You can look up the mass of the sun, but Halley's comet?
Hmm. Well I'll be. Is there anything the internet doesn't know. m1=2.2e14.
m2=1.99e30.
And away you go...
Well, it seems like we've got a gravity dilemma here! Don't worry, I've got you covered with some funny astrophysics! Let's start by using Newton's Law of Universal Gravitation:
F = G * (m1 * m2) / r^2
Where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses, and r is the distance between the two objects.
Since we're comparing the gravitational force between Halley's Comet and the sun at aphelion and perihelion, we can use the formula and solve step by step.
At aphelion, the distance (r) between the comet and the sun is about 4.5×10^12m. While at perihelion, the distance is about 5.0×10^10m.
Now, before we go any further, let me remind you that Halley's Comet is like that one friend who swings by every 75 years, while the sun is the glowing ball of fire that's always there, providing a gravitational force. So, let's calculate!
First, we'll calculate the gravitational force at aphelion. Plugging the numbers into the equation:
F_a = G * (m_comet * m_sun) / r_a^2
Now, because Halley's Comet is relatively small compared to the sun, we'll just consider the mass of the sun:
F_a = G * (m_comet * m_sun) / r_a^2
≈ G * m_sun / r_a^2
Now, we'll do the same for perihelion:
F_p = G * (m_comet * m_sun) / r_p^2
≈ G * m_sun / r_p^2
Now, if you compare the formulas for aphelion and perihelion, you'll notice that the only difference lies in the values of r_a and r_p. The mass of the sun and the gravitational constant are the same in both cases, so their effect on the force is constant.
So ultimately, the closer Halley's Comet gets to the sun, the stronger the gravitational force it experiences. Hence, the force at perihelion will be greater than the force at aphelion.
I hope this explanation brought some sunshine into your gravity calculations! Remember, astrophysics can be a bit of a rocky road, but with a little humor, we can make it a stellar journey!
To compare the gravitational force between Halley's Comet and the sun at aphelion and perihelion, we can use Newton's law of universal gravitation:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force between the two objects.
G is the gravitational constant (approximately 6.67430 × 10^-11 N m^2/kg^2).
m1 and m2 are the masses of the two objects.
r is the distance between the centers of the two objects.
At aphelion:
The distance between Halley's Comet and the sun, r, is equal to 4.5 × 10^12 m.
At perihelion:
The distance between Halley's Comet and the sun, r, is equal to 5.0 × 10^10 m.
To compare the gravitational force, we can divide the force at aphelion (F_aphelion) by the force at perihelion (F_perihelion).
F_aphelion / F_perihelion = [(G * m1 * m2) / (r_aphelion^2)] / [(G * m1 * m2) / (r_perihelion^2)]
Notice that the masses of the two objects (m1 and m2), which are Halley's Comet and the sun, cancel out, so they do not affect the ratio.
Calculating the ratio:
F_aphelion / F_perihelion = (r_perihelion^2) / (r_aphelion^2)
Now we can substitute the values:
F_aphelion / F_perihelion = ((5.0 × 10^10 m)^2) / ((4.5 × 10^12 m)^2)
Simplifying the equation:
F_aphelion / F_perihelion = (25 × 10^20 m^2) / (20.25 × 10^24 m^2)
F_aphelion / F_perihelion = 0.0012345679
Therefore, the ratio of the gravitational force between Halley's Comet and the sun at aphelion to the force at perihelion is approximately 0.0012345679.
To compare the gravitational force between Halley's Comet and the sun at aphelion and perihelion, we can use Newton's law of universal gravitation:
F = G * (m1 * m2) / r^2
where:
F is the gravitational force between two objects,
G is the gravitational constant (approximately 6.67430 x 10^-11 N*m^2 / kg^2),
m1 and m2 are the masses of the two objects, and
r is the distance between the centers of the two objects.
In this case, we can assume the mass of the sun remains constant and calculate the gravitational force exerted by the sun on Halley's Comet at both aphelion and perihelion.
At aphelion, the distance (r) between Halley's Comet and the sun is about 4.5 × 10^12 m.
At perihelion, the distance (r) between Halley's Comet and the sun is about 5.0 × 10^10 m.
Let's denote the force at aphelion as F_aphelion and the force at perihelion as F_perihelion.
To calculate the forces, we need the mass of Halley's Comet. The mass of the comet is not provided in the question, but we can assume it to be negligible compared to the mass of the sun, so we can ignore it for our calculations. This assumption is valid since the mass of the sun is about 1.989 × 10^30 kg, while the mass of Halley's Comet is about 2.2 × 10^14 kg.
Now, let's calculate the gravitational forces using the given distances:
F_aphelion = (G * m1 * m2) / r_aphelion^2
= (6.67430 x 10^-11 N*m^2 / kg^2) * (1.989 × 10^30 kg) * (2.2 × 10^14 kg) / (4.5 × 10^12 m)^2
F_perihelion = (G * m1 * m2) / r_perihelion^2
= (6.67430 x 10^-11 N*m^2 / kg^2) * (1.989 × 10^30 kg) * (2.2 × 10^14 kg) / (5.0 × 10^10 m)^2
After performing the calculations, you will obtain the values for F_aphelion and F_perihelion in newtons. The comparison between the two forces will give you an idea of how the gravitational force changes as the distance varies.