Question

The mass of Saturn is 5.68 x 10^26 kg, and the mass of Neptune is 1.02 x 10^26 kg. The average distance of separation, measured between their centers, is 3.07 x 10^9 km. Locate the center of mass (in m) of the Saturn-Neptune system as measured from the center of Saturn.

Answer 1

The center of mass of the Saturn-Neptune system, as measured from the center of Saturn, is approximately 467 billion meters away.

Step-by-step explanation:

To find the center of mass of the Saturn-Neptune system, we can use the formula for the center of mass between two objects, which is r = (d * mNeptune) / (mSaturn + mNeptune), where r is the distance from the center of mass to Saturn's center, d is the average distance of separation between Saturn and Neptune, and mSaturn and mNeptune are the masses of Saturn and Neptune, respectively.

Substituting the given values:

• Mass of Saturn mSaturn = 5.68 × 1026 kg
• Mass of Neptune mNeptune = 1.02 × 1026 kg
• Average distance of separation d = 3.07 × 109 km = 3.07 × 1012 m (since 1 km = 1000 m)

The center of mass r is calculated as follows:

r = (3.07 × 1012 m * 1.02 × 1026 kg) / (5.68 × 1026 kg + 1.02 × 1026 kg)

r = (3.1314 × 1038 m·kg) / (6.70 × 1026 kg)

r = 4.67044776 × 1011 m

Therefore, the center of mass of the Saturn-Neptune system is located approximately 467 billion meters from Saturn's center.