Star Z has 1/5 the radius of Earth and 1000 times the Earth's mass. If a mass weighs 1.0 N on Earth, what does it weight on Star Z?
The answer is the same as yesterday's.
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To find out what a mass weighs on Star Z, we can use the concept of gravitational force. The weight of an object is given by the formula W = mg, where W is the weight, m is the mass, and g is the gravitational acceleration.
First, let's find the gravitational acceleration on Star Z. The gravitational acceleration is determined by the mass and radius of a celestial body. On Earth, the gravitational acceleration is approximately 9.8 m/s².
Given that Star Z has 1/5 the radius of Earth, the new gravitational acceleration can be calculated using the formula:
g_z = (G * M_z) / (R_z)²
Where G is the gravitational constant, M_z is the mass of Star Z, and R_z is the radius of Star Z.
Since Star Z has 1000 times the Earth's mass, M_z = 1000 * M_e, where M_e is the mass of Earth. Additionally, R_z = (1/5) * R_e, where R_e is the radius of Earth.
Now, substitute the values into the formula to calculate g_z.
g_z = (G * (1000 * M_e)) / ((1/5 * R_e)²)
Next, plug in the values for G (gravitational constant), M_e (mass of Earth), and R_e (radius of Earth) to obtain the value for g_z.
Once you have the value for g_z, you can calculate the weight of the mass on Star Z. Use the formula:
W_z = m * g_z
Substitute the value for m (mass) into the formula to find the weight of the mass on Star Z.