The planet Mars has two moons, phobos and delmos. Phobos has a period of 7 hours, 39 minutes and an orbital radius of 9.4 × 103 km . The mass of Mars is

Question

The planet Mars has two moons, phobos and delmos. Phobos has a period of 7 hours, 39 minutes and an orbital radius of 9.4 × 103 km . The mass of Mars is (A) 6.48 × 1019 kg (B) 6.48 × 1023 kg (C) 6.48 × 1027 kg (D) 6.48 × 1031 kg

Tardigrade Admin · Accepted Answer

T2=(4 π2/G Mm) R3 ⇒ Mm=(4 π2/G T2) R3 =(4 ×(3.14)2 ×(9.4)3 ×(106)3/(6.67 × 10-11) ×(459 × 60)2)=6.48 × 1023 kg

Q. The planet Mars has two moons, phobos and delmos. Phobos has a period of $7$ hours, $39$ minutes and an orbital radius of $9.4 \times 1 0^{3} km .$ The mass of Mars is

$6.48 \times 1 0^{19} k g$

$6.48 \times 1 0^{23} k g$

$6.48 \times 1 0^{27} k g$

$6.48 \times 1 0^{31} k g$

$T^{2} = \frac{4 π ^{2}}{G M _{m}} R^{3} \Rightarrow M_{m} = \frac{4 π ^{2}}{G T ^{2}} R^{3}$
$= \frac{4 \times ( 3.14 ) ^{2} \times ( 9.4 ) ^{3} \times ( 1 0 ^{6} ) ^{3}}{( 6.67 \times 1 0 ^{- 11} ) \times ( 459 \times 60 ) ^{2}} = 6.48 \times 1 0^{23} k g$

Q. The planet Mars has two moons, phobos and delmos. Phobos has a period of 7 hours, 39 minutes and an orbital radius of 9.4×103km. The mass of Mars is

6.48×1019kg

6.48×1023kg

6.48×1027kg

6.48×1031kg