Black Holes are suspected when a visible star is being noticeably pulled by an invisible partner that is more than 3 times as massive as the Sun. A red giant star is accelerated in a linear direction by gravity at 0.075 m/s2 towards an object that is 9.4 x1010 m away.
a) What is the mass of the invisible star? Answer using scientific notation (eg. 1e+10)
b) By what factor is the star more massive than our Sun? Answer in decimal.
F = GMm/r^2
a = F/m = GM/r^2 = 6.673*10^-11 * M / (9.4*10^10)^2 = 0.075
M = 9.931*10^30
M/sun = 9.931*10^30 / 1.989*10^30 = 4.993
so, the red giant is 5 times as massive as Sol.
a) Well, if the invisible partner is making the red giant star move around like a puppet, we need to calculate its mass. We can use the formula for gravitational acceleration:
a = (G * M) / r^2
Where:
a = acceleration (0.075 m/s^2)
G = gravitational constant (6.67430 × 10^-11 m^3 kg^-1 s^-2)
M = mass of the invisible star (unknown)
r = distance between the two objects (9.4 x 10^10 m)
Rearranging the equation, we get:
M = (a * r^2) / G
M = (0.075 * (9.4 x 10^10)^2) / 6.67430 × 10^-11
Calculating all of that, we find that the mass of the invisible star is approximately 4.49 x 10^31 kg.
b) To find out how massive the invisible star is compared to our Sun, we can simply divide the mass of the invisible star by the mass of the Sun:
Mass factor = M_invisible / M_Sun
Mass factor = 4.49 x 10^31 kg / 1.99 x 10^30 kg
After some math magic, we uncover that the invisible star is roughly 22.5628 times more massive than our Sun. So, hold onto your space helmets, because that's quite a heavyweight!
To find the mass of the invisible star, you can use the law of universal gravitation equation. The equation is given by:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force
G is the gravitational constant (6.67430 × 10^-11 N(m/kg)^2)
m1 and m2 are the masses of the two objects
r is the distance between the centers of the objects
In this case, the force acting on the red giant star is the gravitational force pulling it towards the invisible partner.
a) To find the mass of the invisible star, we need to rearrange the equation to solve for m2:
m2 = (F * r^2) / (G * m1)
Plugging in the given values:
F = 0.075 m/s^2 (acceleration)
r = 9.4 x 10^10 m (distance)
G = 6.67430 × 10^-11 N(m/kg)^2 (gravitational constant)
m1 is not given in the question, so we cannot calculate the exact mass of the invisible star without that information.
b) Since we don't have the mass of the invisible star directly, we can only determine the mass as a factor compared to the Sun. To do this, we can use the ratio of the mass of the invisible star to the mass of the Sun:
mass factor = m2 / mass of the Sun
Since the question states that the invisible star is more than 3 times as massive as the Sun, we can express this in decimal form.
Unfortunately, without knowing the exact mass of the invisible star or the mass of the Sun, we cannot calculate the exact factor.