Two stars with masses 2.75 x 10^30 kg and 5.92 x 10^30 kg form a binary system. If the two stars have an average separation of 7.28×10^8 km, compute the magnitude of the gravitational force in Newtons between the stars. Express your result in scientific notation and to three significant digits
F = GM1M2/r^2
plug.chug.
To compute the magnitude of the gravitational force between the two stars, you can use Newton's Law of Universal Gravitation:
F = G * (m1 * m2) / r^2
where F is the magnitude of the gravitational force, 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 stars, and r is the average separation between them.
Let's plug in the given values:
m1 = 2.75 x 10^30 kg
m2 = 5.92 x 10^30 kg
r = 7.28 x 10^8 km
To convert km to meters, multiply by 1000:
r = 7.28 x 10^8 km * 1000 = 7.28 x 10^11 m
Now, let's substitute these values into the formula and calculate the magnitude of the gravitational force:
F = (6.67430 x 10^-11 N m^2 kg^-2) * ((2.75 x 10^30 kg) * (5.92 x 10^30 kg)) / (7.28 x 10^11 m)^2
Simplifying,
F = (6.67430 x 10^-11) * (2.75 x 10^30) * (5.92 x 10^30) / (7.28 x 10^11)^2
= 2.1637159 x 10^20
Therefore, the magnitude of the gravitational force between the two stars is approximately 2.16 x 10^20 Newtons to three significant digits.
Note: The calculated result should be expressed in scientific notation with three significant digits, with the exponent value adjusted accordingly.