Rank the objects based on the strength of the gravitational force that would be felt by a spacecraft traveling at a distance of 10 AU from the center of each of the objects, from weakest to strongest.
1)red giant mass: 1Msun radius: 100Rsun
2)sun
3)white dwarf mass: 1msun radius: 0.01Rsun
4)black hole mass: 1msun radius: (event horizon) approx. 3 km
Please help me rank them, I though that it would be by the radius since as radius increases , gravitational pull decreases and the mass is the same i ranked it weakest to strongest 1,2,3,4 but i think the black hole is not supposed to be strongest since its 10 AU and its only strong at the event horizon.. please help!
all of the gravitational force would remain the same aka. all of them are the same because they are at the same distance 10AU
I JUST DID THIS PROBLEM AS WELL
got right
"as radius increases , gravitational pull decreases"
This rule applies to measurements made at the surface of objects with the same mass.
If we restrict ourselves to Newtonian mechanics, which should apply at 10 AU, and if the masses are all equal at 1M sun, the gravitational pull (on a relatively small space-ship) should be all equal, depicted by the Newton's law of universal gravitation:
GMm/r².
that doesnt apply at 10AU.
To rank the objects based on the strength of the gravitational force felt by a spacecraft at a distance of 10 AU from their center, you need to consider the equation for the gravitational force:
F = G * (m1 * m2) / r^2
where F is the force, G is the gravitational constant, 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, you have a spacecraft at a fixed distance of 10 AU from the center of each object. Therefore, you can compare the masses of the objects to determine their relative gravitational pull.
Let's analyze each object based on their mass:
1) Red Giant: The mass is given as 1Msun (which is the mass of our Sun). The radius of the object does not directly affect the gravitational force experienced by the spacecraft at a fixed distance. Therefore, we can ignore the radius. So, the gravitational force will be the strongest among all the objects.
2) Sun: The mass is the same as the Red Giant (1Msun), so the gravitational force will be the same. Therefore, it ranks second.
3) White Dwarf: The mass is given as 1msun (which is 1/1000th of the Sun's mass). Since the mass is smaller, the gravitational force will be weaker compared to the Sun. So, it ranks third.
4) Black Hole: The mass is also given as 1Msun, which is the same as the Red Giant and the Sun. However, black holes are known for their extremely high gravitational pull due to their compactness. Even though the black hole's gravitational force is strong, it is only influential within its event horizon. At a distance of 10AU, it will have a weaker gravitational force compared to the Red Giant and the Sun. Therefore, it ranks last.
So, the correct ranking based on the strength of the gravitational force felt by the spacecraft from weakest to strongest would be:
3) White Dwarf
2) Sun
4) Black Hole
1) Red Giant