Physics... help me.. too difficult. :(

Question

1) NASA is going to explore Venus with a 7500kg spacecraft. The spacecraft was put into orbit at 650km above the surface of the Venus. How much is the gravitational force on the satellite?(Mass- 4.87 x 10^24kg, Equatorial Radius- 6.05 x 10^6m, orbital period- 224.7days, mean orbital radius- 1.08 x 10^11m)

 

 

2) How much is the mean orbital radius for Planet X? (Mass - 8.20 x 10^23kg, Orbital Period - 450days)

Answer 1

1)

 

Calculate the  gravitational force by using the following formula:

F = G Mm/(r+h)^2

Mass of the venus M =4.87 × 10²⁴   kg

Universal gravitational constant, G = 6.673×10^-11 m³ kg^-1 s^-2

Mass of the sattelite, m =7500 kg

Radius of the the venus, r = 6.05 x 10⁶ m

Height of the sattelite from venus orbit, h = 650 km =650000 m

 

F =( 6.673×10^-11) (4.87 × 10²⁴)(7500)/(6.05 x 10⁶+650000)^2

   =( 243731.325×10¹³)/(448.9 x 10¹¹)

  =54295.24 N

 

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2)

Calculate the  mean orbital radius of the planet by using the following formula:

r =∛( T ²GM/4 π²)

Mass of the planet, M  = 8.20 × 10²³   kg

Universal gravitational constant, G = 6.673×10^-11 m³ kg^-1 s^-2

Orbital Period,T =450 days = 450×24×3600 sec

r =∛( T ²GM/4 π²)

   =∛( (450×24×3600) ²(6.673×10^-11)(8.20 × 10²³)/4 π²)

   =128 x 10⁶ m