Question

If the mass of Jupiter is defined as 1 M_j = 1.90 ✕ 10^27 kg, what is the mass of Saturn (5.68 ✕ 10^26 kg) in units of M_j?

What is the mass of Earth (5.97 ✕ 10^24 kg) in M_j?

What is the mass of Neptune (1.02 ✕ 10^26 kg) in M_j?

Answer 1

To convert masses to units of M_j, we need to divide the given mass by the mass of Jupiter:

1 M_j = 1.90 x 10^27 kg

(a) Mass of Saturn in M_j:

Mass of Saturn = 5.68 x 10^26 kg

Mass of Saturn in M_j = (5.68 x 10^26 kg) / (1.90 x 10^27 kg/M_j)

= 0.299 M_j

Therefore, the mass of Saturn in units of M_j is approximately 0.299 M_j.

(b) Mass of Earth in M_j:

Mass of Earth = 5.97 x 10^24 kg

Mass of Earth in M_j = (5.97 x 10^24 kg) / (1.90 x 10^27 kg/M_j)

= 0.00315 M_j

Therefore, the mass of Earth in units of M_j is approximately 0.00315 M_j.

(c) Mass of Neptune in M_j:

Mass of Neptune = 1.02 x 10^26 kg

Mass of Neptune in M_j = (1.02 x 10^26 kg) / (1.90 x 10^27 kg/M_j)

= 0.0537 M_j

Therefore, the mass of Neptune in units of M_j is approximately 0.0537 M_j.

Answer 2

Answer: 1. Mass of Saturn in terms of Jupiter mass:

Saturn's mass = 5.68 × 10²⁶ kg

Jupiter's mass, MJ = 1.90 × 10²⁷

Therefore, Saturn's mass in terms of MJ = Saturn's mass/1.90 × 10²⁷

= 0.299 MJ

Therefore, Mass of Saturn is smaller than and is equal to 0.299 times mass of Jupiter.