Question

A planet with mass 6.5x10^27 kg is in a circular orbit around a star whose mass is 4.0 x 10^30kg. The radius of the star is 7.5 x 10^7m. the star and planet move in circular orbits around their center of mass and the distance between their centers is 6.3 x 10^10m. What is the distance from the center of the star to the center of mass of the system consisting of the star and planet?

Answer 1

The distance from the center of the star to the center of mass of the star-planet system is calculated using the center of mass formula and the given masses and distance between the star and planet. The calculated distance is approximately 1.02×10^8 meters.

Step-by-step explanation:

Calculating the Distance to the Center of Mass:

To find the distance from the center of the star to the center of mass of the star-planet system, we can apply the concept of center of mass (COM). The center of mass of a two-body system is calculated using the formula:

rCOM,star = (mplanet × R) / (mstar + mplanet)

Where:

• mplanet is the mass of the planet (6.5×1027 kg),
• mstar is the mass of the star (4.0×1030kg), and
• R is the distance between the centers of the star and planet (6.3×1010m).

Plugging in the values we get:

rCOM,star = (6.5×10^27 kg × 6.3×10^10m) / (4.0×10^30kg + 6.5×10^27 kg)

Performing the calculation gives us:

rCOM,star ≈ 1.02×10^8 meters

The distance from the center of the star to the center of mass of the system is therefore approximately 1.02×10^8 meters.