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Vedmedyk [2.9K]
2 years ago
12

The mass of the Sun is 2 × 1030 kg, and the mass of Saturn is 5.68 × 1026 kg. The distance between Saturn and the Sun is 9.58 AU

. Veronica is solving the following equation to calculate the orbital period of Saturn, but there is an error in the equation. T = What should Veronica change to correct the equation?
change the position of 2 x 1030 kg and 9.58 AU
change 2 x 1030 kg to 5.68 x 1026 kg
change the square root to a cube root
change 9.58 AU to the distance in meters
Physics
2 answers:
kykrilka [37]2 years ago
7 0

The correct answer is D.

Maurinko [17]2 years ago
3 0
The formula for computing the orbital time period of a body is given as:

T² = 4π²r³ / GM

where T is the time period, r is the distance between the two bodies, G is the gravitational constant and M is the mass of the body that is being orbited. If we compute this time using SI units, the working is:

9.58 AU is 1.43 x 10¹² meters

T = √[(4*π²*(1.43 x 10¹²)³) / (6.67 × 10⁻¹¹ * 2 x 10³⁰)]
T = 9.30 x 10⁸ seconds which is approximately 29 years


Using the astronomical units, distance is in astronomical units and the mass is in solar masses. In these conditions, the ratio:
4π²/G = 1 so

T² = a³ (since the solar mass of the sun is 1)

T = √(9.58)³
T = 27 years
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